my husband and I will have a week in New York in June and our preferred method of transport in a new city is walking. (I also like regularly spaced coffee shops).
Wow walking is definitely THE way to go to explore the city. I just starting from one end of the island and heading to the other!
From East to west, a good starting point is to find yourself in the East Village and then walk along Houston street through to Soho and onward to Greenwich village. These are some of the more eclectic neighbourghoods in the city with a great funky vibe.
Otherwise, if you're REALLY looking for a walk, start on Broadway in the Chinatown area and just stick to it heading North. You'll be amazed at how this ONE street changes so dramatically...from the filthier street in Chinatown to the trendy shops in Soho through to the malls in Midtown and all the way up to brightlights of Times Square and even up through to the brownstones on the Upper West Side!! about 10 years ago
Great recommendations above! A good map is all you need and/or a smart phone with cool apps like Urbanspoon, yelp, and opentable to help you with the food/cafe pitstops. My fave walk is from Unuin Square down Braodway towards Canal Street and through Chinatown. Keep going to City Hall and then walk over the Brooklyn Bridge and over to Brooklyn Heights. If you have the stamina keep going to Carroll Gardens and Smith Street where there are terrific restaurants (The Grocery is one of NYC's best-make reservations!) about 10 years ago