Manhattan would be one place where it would be interesting to have yourself hooked up to a pedometer to see just how many steps you can walk in a day. Although we took subways when we were going a significant distance, a large part of our time was spent walking around all the various districts, and I'd definitely recommend it as the best way to see the city and get a feel for what it's really like. The Lonely Planet New York City guide has walking tours of most of the main districts, which are a good starting point - we used at least part of these in Chinatown, Little Italy, and Brooklyn Heights. A lot of the time, though, it's just fun to wander and see where things take you. We usually had a final goal in mind but went down any street that appealed to us and in the process saw some great buildings and sights that we would probably otherwise have missed.
East Village is one of the best places for wandering around. We went there on a Saturday, and it was really chilled out - nothing like London on a Saturday morning! St Mark's Place is a must - a beautiful tree-lined street with some great thrift shops and and the Physical Graffiti building of Led Zeppelin fame that is now a thrift shop. There's a great selection of bars, diners, and cafes in East Village, so it's good night or day - although when we went down there at about 11pm on Sunday, it was pretty quiet and a lot of places were closing - but, as usual, you always find somewhere open in New York, and it's usually just what you were looking for!
Chinatown on a Saturday afternoon was quite chaotic, especially as there was an event going on promoting all the restaurants in the area, so there were hundreds of people on the streets selling food and a fantastic atmosphere. Little Italy blends into the outskirts of Chinatown and is a great place to sit at one of the pavement cafes and watch Manhattan walk by for a while.
Greenwich Village seemed to have lost a lot of its past bohemian feel on first entering it, and it has definitely been usurped nowadays by East Village in that respect. But it's worth a trip to Washington Square Park, which, when we got there at dusk, was full of street performers, beautiful lanterns dotted around, and people sitting around, playing guitars and chilling out. It was a wonderful and very un-urban thing to experience in the middle of a city, especially in the evening in a park when they are more usually deserted and not really advisable to enter! The financial district is another one to wander through.
We came across ground zero purely by accident, and there is an intense energy resonating from the site still. Plans can now be seen at the site of the proposed memorial park that is to be built there, and the subway there is now up and running.
Of course, if you're going to walk in Manhattan, then the obvious place to do it is Central Park. We spent a couple of hours wandering around and only made it about a third of the way up, past the Woolman rink, although sadly it wasn't ice-skating weather, and past people dotted around reading books and doing yoga in Sheep Meadow and on up to Strawberry Fields opposite the Dakota Building and the flower adorned Imagine Mosaic commemorating John Lennon's favourite bit of the park. The design of the park has succeeded in what I presume was its intention of being a rural oasis in the midst of the vast expanse of the city around it. It would be a great place to just go and hang around and wander slowly - if only there weren't so damn many other things to do in this city! But whether you're travelling at marching pace or strolling leisurely, this city is one that is conducive to walking. It's easily navigable and compact enough to be able to see a lot of sights in a relatively short space of time and a lot of diverse and really interesting areas.