Fashion Street, always bustling with shoppers, has hundreds of stalls containing anything shoppers might want to buy — dresses, T-shirts, jeans and accessories.CreditPhilippe Calia for The New York Times

The profile of the Dharavi slum in Mumbai, one of the most densely populated neighborhoods in the world, may have risen when it was showcased in the Oscar-winning movie “Slumdog Millionaire,” but my tour guide didn’t particularly care about that at the moment. What concerned him more was the pejorative nature of the word “slum” and how outsiders perceived Dharavi, an area smaller than New York City’s Central Park but where about a million people live and work.

“We don’t want people to think slums are dangerous and full of lazy people,” said Hitesh Vaidya, a guide for Reality Tours and Travel. The reality of daily life in Dharavi is sobering, however: Laborers work in unsafe conditions, and a lack of basic services like clean water and sanitation facilities endangers the health of residents. Mr. Vaidya and I spent the next couple of hours touring the many different industries and businesses within Dharavi, which included plastics recycling, textile manufacturing and food production. I left with a better knowledge of both the poverty and industriousness of Dharavi, as well as an understanding of Mr. Vaidya’s point: that the two are not mutually exclusive.

The Dharavi slum, where about a million people live and work.CreditPhilippe Calia for The New York Times

Mumbai (sometimes called by its former name, Bombay) is an electric and complicated city, an extraordinary place, both uplifting and heartbreaking. Its eclectic composition of different groups and cultures makes it a difficult city to define, but for many, it’s a city that represents possibility. Dharmesh Gandhi, a friend who lives in Mumbai, offered his take on India’s financial center and one of the world’s most populous cities: “It’s like New York,” he said. “Everything is happening here, so everyone wants to come here.”

After a four-day visit this past October, it was easy to see why: The shopping and entertainment options were excellent, and opportunities for great dining were second-to-none. And while the rupees flow freely in Mumbai, I was able to keep my spending under control.

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A couple of logistical items: My flight, booked through Jet Airways, cost a bit over $200 for a one-way flight from Sri Lanka. As I was re-entering India, I had to produce my double-entry e-visa once more to passport control. My Uber ride from the airport was about 370 rupees, or a little more than $5. If you’d prefer not to use Uber, another popular service is Ola Cabs. I used both while in Mumbai, typically opening both apps and using whichever had a car closer to me. The ubiquitous tuk-tuk is conspicuously absent in much of Mumbai (“The traffic here is bad enough,” Mr. Gandhi told me). In central Mumbai, you’ll just see regular taxis. Fortunately, they’re metered, with fares beginning at 22 rupees.

I was well-located in the Fort neighborhood of the city, close to the Chhatrapati Shivaji Maharaj Terminus railway station, the huge Victorian landmark constructed in the late 19th century. My quarters at the Hotel Residency Fort, Mumbai, booked for $52 a night on, were modest luxury, roomy and air-conditioned, and with free breakfast.

A walk around the neighborhood was the first order of business: A stop by Mumbai’s first Anglican church, St. Thomas Cathedral, established in 1718, was followed by a visit to the free Jehangir Art Gallery near Wellington Fountain. I enjoyed the Nayanaa Kanodia exhibition, “The Quintessential Woman: A Celebration,” which featured oil paintings and drawings celebrating feminism. Another exhibition, “Rural Beauty,” featured darker, more sensual pencil and pastel works by Parshuram B. Patil.

There are numerous fine museums in Mumbai, including Chhatrapati Shivaji Maharaj Vastu Sangrahalaya (formerly known as the Prince of Wales Museum of Western India). Admission is 500 rupees, plus an additional 50-rupee fee to take cellphone photos. The main hall of the museum, which features Rajastani temple columns and wooden railings from a nobleman’s home, is topped with a great Islamic dome — a nod to Mumbai’s diverse history.

There are some wonderful statues of Indian deities on the ground floor — Shiva, Ganesh, Brahma and Vishnu, some dating as far back as the sixth century. I also enjoyed looking at a series of paintings from the late 17th and early 18th centuries, done in the Rajasthani Bikaner style, particularly one depicting a scene from the Mahabharata epic.

My favorites, though, were probably the later work of Jehangir Sabavala, a Mumbai-born artist who died in 2011 at age 89. His paintings, which intriguingly join East with West, have elements of both Cubism and Impressionism. I particularly liked “The Eye,” as well as his somber “The Raven,” 2010 works that were two of Sabavala’s final pieces.

The Dr. Bhau Daji Lad Mumbai City Museum, which claims to have been Mumbai’s first, opened in 1872.CreditPhilippe Calia for The New York Times

The most interesting museum I visited, however, proved to be the Dr. Bhau Daji Lad Mumbai City Museum, which claims to be Mumbai’s very first, established in 1872 (100 rupees admission). The building itself is quite beautiful, and houses interesting artifacts like old model ships, ganjifa — round playing cards that became popular under Mughal emperors in the 16th century — and examples of pottery from the Sir J.J. School of Art near the turn of the 20th century. Particularly interesting was an exhibition documenting the movement of peoples to Mumbai over the years, from the Kolis fishermen of Gujarat in the 13th century to the Parsi, Surati and Khoja people that immigrated with the rise of the East India Company.

But it’s not just the past that impresses in Mumbai — the present is pretty happening, too. I headed to the club the Quarter one evening to catch a show with Azamaan Hoyvoy and his pseudo-funk trio (750 rupees for a standing ticket). They grooved through a number of pretty good covers, including “How Deep Is Your Love” and Allen Stone’s “Unaware.” Cocktails at the Quarter run in the 600 rupee range, but you can get a Kingfisher beer for 275.

I spent another evening at Shanmukhananda Hall, a large auditorium near the King’s Circle train station, to take in a Lucky Ali concert (1,500 rupees, purchased through the website Book My Show). Lucky Ali, a Mumbai-born musician, went through crowd-pleasing soft rock favorites with a six-piece band. Between numbers, he took the opportunity to speak on various issues. “If Ganga goes, where do we go?” he asked, referring to the Ganges River. “I think half of you probably haven’t even been there. Go there! Plant some trees or something.”

People line up to enter the Siddhi Vinayak Mandir. The top of the temple is visible in the distance.CreditPhilippe Calia for The New York Times

About two-and-a-half miles to the southwest is Siddhi Vinayak Mandir, a beautiful temple dedicated to Ganesha and an essential place of worship for many Mumbai Hindus. I arrived just in time one evening for a puja, and after leaving my shoes at a counter outside, was ushered in to the sound of clapping, drums, bells and the smell of incense. A small, serene-looking Ganesha statue sat among orange and white flowers while a group of about 150 of us stood engaged in an intense, rhythmic call-and-response that changed tempos and melodies throughout the course of the next 30 minutes. For those looking to worship in a hurry, a “quick darshan” line can be entered for a payment of 50 rupees.

Any explorer of Mumbai will eventually need to try one of thousands of street vendors and restaurants that grace the city. Fortunately, there is no shortage of good options, and nearly every price point is covered. The Bombay street sandwich is one you’ll see everywhere and, if you’re feeling adventurous, certainly worth trying. A typical example features sliced cucumber, potato, onion, tomato and beetroot on toasted bread, served with a variety of spicy chutneys. At 25 or 30 rupees, it’s an absolute steal.

Mumbai’s reputation for street food par excellence is well deserved, and on Sheikh Memon Street, near the Juma Masjid mosque, I indulged in another treat: a plate of dahi puri (40 rupees), savory chickpeas stuffed into flaky puri shells, drenched in tart yogurt and dusted with spices and herbs. And no Mumbai street food discussion is complete without mentioning vada pav, the quintessential carbohydrate bomb that features a fried potato fritter squished into soft white roll (about 10 rupees, and it can be found all over).

The city does upscale dining with equal aplomb. Prateek Sadhu and Aditi Dugar own Masque, an elegantly repurposed industrial space that serves a 10-course tasting menu every day except Monday. The wine pairing alone, however, costs 6,000 rupees — it’s not exactly a place for penny-pinchers. Fortunately, Masque offers a bar menu for walk-ins like me looking for a lighter meal.

A very good sour eggplant toast (350 rupees), sweetened with tamarind and covered with caramelized onions, functioned as a kind of tangy eggplant pâté. A twist on pani puri, the classic street food, filled the thin shells with a cactus salad and corn mousse (350 rupees). Something described as pork okonomiyaki (500 rupees) really was like a sweet-glazed pork taco, competently prepared and served with a nice cabbage slaw. My server, Ayush, was particularly good and made me feel right at home.

Lunch at Gurukripa, a vegetarian restaurant in the Sion neighborhood.CreditPhilippe Calia for The New York Times

Somewhere in the middle, you’ve got Gurukripa, an all-day casual vegetarian restaurant in the Sion neighborhood. There’s an exceptionally good pav bhaji (96 rupees), a tomato-y mash of spiced vegetables served with a slab of rapidly melting butter. White rolls, crunchy papadum and a sharp onion salad round out the meal. Or there’s Ling’s Pavilion, a Mumbai institution, where the steamed pork with salted fish (500 rupees) and creamy fried corn curd (275 rupees) will help explain the country’s love of Chinese food.

And don’t forget the shopping. At the excellent Kitab Khana bookstore, I perused the sizable section entitled “Books on Gandhi and by Gandhi” before settling on Mohandas K. Gandhi’s autobiography, “The Story of My Experiments with Truth,” for just 156 rupees. Another day, I set out in search of spices and ended up at Lalbaugh Market near Chinchpokli Station. Wandering down Dinshaw Petit Road, I followed the sound of loud, metallic pounding until I ended up at Vishwas, a specialty spice store where a shopkeeper was in the process of mashing a red substance into fine powder. I asked for haldi, or turmeric, and the man behind the counter spooned a 200-gram plastic bagful for 60 rupees.

But the best way to get a feel for the city might be to walk along Fashion Street on a weekend afternoon. Fashion Street is on the western edge of Fort, along Mahatma Gandhi Road, flanking a big public park, Azad Maidan, and branching off into Karmaveer Bhaurao Patil Road to the south. On the street, packed solid with shoppers, are hundreds of stalls containing anything you could possibly want to wear — dresses, T-shirts, jeans and accessories.

Groups of young men play cricket all around Fashion Street.CreditPhilippe Calia for The New York Times

I picked up a shirt for 250 rupees and, after a bit of haggling over the initial ask of 1,000, walked away with a pair of jeans for 600 rupees. Satisfied with my haul, I walked through the Karnatak Sports Ground, where organized teams were playing games of cricket. As the sun began to set, I crossed the street to Azad Maidan, past food vendors selling snacks and couples lounging on the grass while groups of boys played decidedly more casual pickup cricket games with tennis balls.

Over a good dinner at the Parsi restaurant Ideal Corner, I reflected on my time in a city that has so much to offer — too much for one trip, certainly. Some trips are draining, but Mumbai left me feeling energized. I would have to return again to this dynamic city, and soon.

Read about previous stops on the Frugal Traveler’s trip to India
Cups of Tea, Pashminas and Momos, Seeing India’s Himalayas on a Budget

In Kolkata, a Love of Literature, Fried Street Food and, Mostly, Sweets