Most of sprawling Delhi is best navigated on wheels—hire a car, taxi, or auto-rickshaw to get around. In contrast, the narrow lanes of Old Delhi are a walker's delight, though you can hop on a cycle rickshaw if you get tired. Most people speak workable English, so don't assume there will be an insurmountable language barrier.
The challenge Delhi presents is to find areas—beyond the Old City—in which walking is a viable mode of exploration. One of these areas is the central British-built commercial hub, Connaught Place. "CP" is a tourist magnet for its travel agent bucket shops, restaurants, and shops, as well as proximity to a number of mid-range and budget hotels. It’s also the location of Delhi’s main Metro station and can be a pleasant area to meander along colonnaded circles, or people-watch in the central park. There are plenty of shopping options nearby, including the street market, Janpath, where everything from brightly colored kolhapuri slippers to designer overstock to incense and natural soaps can be found. Keep in mind that even though it's commonly referred to as Connaught Place, the name was officially changed to Rajiv Chowk, which is what you'll see on metro stops and maps.
Around the hubs of Connaught Place and India Gate is the British-built city. This is the seat of the Indian government, with Rashtrapati Bhavan (the Presidential Palace), the North and South Secretariats, Sansad Bhavan (Parliament House), and India Gate (a monument to British Indian Army soldiers killed in World War I and the Afghan wars) within a tight radius. Getting ice cream at India Gate’s huge lawns or boating in the ornamental canals here are "very Delhi" things to do. Many museums are nearby, including the National Gallery of Modern Art and the National Museum.
Also here are the palatial residences of the affluent and lavish government bungalows. Khan Market, one of Asia’s most expensive retail locations, is perfectly at home in this setting. It’s also the place where Delhi’s expats feel most at home, with its coffee shops and multiple ATMs. Down the road is Delhi’s green lung, Lodhi Gardens, and several cultural centers, including the elite’s mainstays the India International Centre and the India Habitat Centre (performances are pretty much on tap, especially in winter).
The mostly residential areas of South Delhi, West Delhi, North Delhi, and East Delhi (across the Yamuna) all have their own flavor, but visitors are most likely to venture into the neighborhoods, markets, and monuments of the first, roughly defined as south of Lodhi Road. In between semi-gated colonies are a good mix of urban villages, hectic alleyways, posh markets, and office complexes. Some of the city’s oldest monuments can be found here, as well as some of its newest monuments to modernity: the massive malls squatting southward, en route to mega-suburb Gurgaon. The hippest of Delhi’s hot spots though, is not a mall, but a gentrified urban village—Hauz Khas Village—with boutiques and trendy restaurants nestled atop each other along narrow alleys, next to a 13th-century reservoir and several Sultanate ruins.