In the movie “Dirty Pretty Things,” hardworking young immigrants in London wish the city would be more like New York – where “they put lights in the trees in winter and where you can skate in the parks.” I, however, often wish New York were more like London – where so many museums and exhibits are free or very cheap, where the Tube takes you just about anywhere, and where they’ve figured out how to redevelop their once desolate waterfront into thriving neighborhoods.

London’s 2,000-year-old rapport with the Thames is even more profound than New York’s bond with the Hudson and East rivers. Yet London has been able to move on decisively from its shipping heritage – many of its docks and yards were, of course, virtually destroyed by the Luftwaffe during World War II.

London’s response has been to build new neighborhoods on the Thames – and then sustain them by opening innovative cultural facilities to attract tourists, who in turn patronize the budding restaurants, bars, and boutiques. This strategy also relieves some pressure on the overly congested West End, which often feels on weekends like a rock concert has just let out.

Even 20 years ago it would have been unthinkable to abandon the West End for the East End and beyond. But the hip Access London guide, whose mission encompasses all of London, now gives a page to the Docklands, headlining it “Vibrant Revival” and encouraging tourists to give it a try. Access argues that the 8.5-square-mile area is a wonderful place to walk, feast, sightsee, relax, and enjoy an “unparalleled look at the luminous Thames.”

New Yorkers may remember the Docklands as the project that nearly bankrupted the Canadian Reichmann family – one-time developers of several buildings in Battery Park City. And indeed, Canary Wharf’s Cesar Pelli-designed building looks distinctly familiar. Docklands’ charm, however, lies not in its huge buildings but in the nearby converted warehouses, restored brick houses, and gorgeous low-rise developments full of shops and services. On a recent visit, we walked, but for those who would prefer to ride, the area is well served by the Dockland Light Rail – yet another London example of how to nourish new neighborhoods.

An excellent start is at the Museum in Docklands, located in a late Georgian warehouse, which presents public exhibits and lectures on London’s port. It doesn’t shirk controversial topics, holding an event on March 15, for example, called “They Cut Their Own Throats,” on the dockworker strikes of the 1960s and 1970s that ended up shutting down the port. (Museum in Docklands, No. 1 Warehouse, West India Quay, Hertsmere Rd., 0870-444-3857, www.museumindocklands.org.uk; children are admitted free, adults pay $9.)

We meandered along the Thames until we ended up in Wapping, once famous for Rupert Murdoch’s triumph over the newspaper unions and now known for fabulous apartments, art galleries, and renovated ancient pubs. A good place to eat is Prospect of Whitby (57 Wapping Wall, between Glamis Road and Garnet Street), which started out in 1520 as the Devil’s Tavern, a gathering spot for smugglers. Its food is excellent, and its views of the Thames are said to be the ones that inspired Whistler and Turner.

From Wapping we walked the long way back to Greenwich, which is stuffed with treasures, including magnificent buildings erected on top of destroyed masterpieces. The beautifully tiled Greenwich Footway Tunnel links Greenwich to the Isle of Dogs, whose shape is a bit like Brooklyn’s Red Hook. Close to the tunnel, the Cutty Sark, the fastest of the 19th century tea clippers and now a museum, is dry-docked (Greenwich Pier, King William Walk, 020-8858-3445). Further inland the National Maritime Museum (Park Row, Greenwich, 020-8312-6632) holds the world’s finest collection of globes, and the Royal Observatory (Park Row, 020-8312-6565) is home to the Prime Meridian, where you straddle two time zones. (The Greenwich Meridian and Greenwich Mean Time remain the world’s standards, even though the British Empire that Greenwich helped launch is long dispersed.)

From Greenwich, you can take a boat to Westminster or hop on the light rail, which will connect with the Underground. We connected to the red line (Central) to see St. Paul’s, since we were still in a Christopher Wren mood. Londoners complain about the depredations of towers and new buildings around the great cathedral – the area had been flattened by German bombs – but St. Paul’s always looks to me like a sacred spaceship, utterly serene on its site. Nearby is Wren’s St. Mary-Le-Bow, built in 1670. Anyone living within sound of the Bow Bells can be self-designated a Cockney.

On Sunday morning at 8:30 we headed back for St. Paul’s nearly professionally sung High Mass. After Mass, we wanted to find the Museum of London (London Wall, 020-7814-5778, www.museumoflondon.org.uk), shown by our map to be nearby. No taxis were in sight, but a bus driver spotted our aimless wandering and told us he could take us within a block of the museum. Even then, we spent another 15 minutes trying to find our way around the deserted streets of the Barbican Centre – a renowned early 1980s mixed-use development that brings to mind Fritz Lang’s “Metropolis.” More than once we got caught on narrow traffic islands, able to see the museum above us but totally unsure of how to reach it. How could they have built something this hostile to London’s streets? Nonetheless, the museum is worth the trouble. Telling London’s story from the 43 C.E. Roman invasion forward, the museum is particularly vivid on landscape and geography.

We spent our last day doing what most people do on their first: heading to Hungerford Bridge to look up and down the snaking Thames. We could see St. Paul’s in the distance, looking every inch magnificent, and the Docklands far off to the right. The London Eye, the 450-foot-tall Ferris wheel at Jubilee Gardens (adults, $21; children 5-15, $10; children under 5, free), has just reopened, giving passengers 30 minutes of incomparable views. The Thames and its city have never looked better.

February and March is a great time to go to London because airfares are cheap and the weather – cool and misty – is fine for walking. We bought our tickets at the last minute, snaring round-trip fares of $282 each on American Airlines to Heathrow. The planes were empty going and returning, so we were pleased that we had not upgraded to the completely filled first-class section.

We had decided to stay centrally in Mayfair since we knew we wanted to hit the big shows at the National Portrait Gallery (Lee Miller and Frida Kahlo) and at the Royal Academy of Arts (Turks). The Washington Mayfair (5 Curzon St., 020-7499-7000) provides large, nicely furnished rooms for $320, including full English breakfast. The nearby Mayfair Hilton is lovely and non-Hiltonish. The Holiday Inn Mayfair offers very low rates online and seems to be the hotel of choice for large European families and tour groups.

Shepherd Market across Curzon Street has a dozen excellent restaurants, including the Al Hamra (31-32 Shepherd Market), which may have the best Lebanese food in London, and the Miyama (38 Shepherd Market, 020-7493-1954), which serves extraordinary Japanese food.