Better yet, walk everywhere. Now, it's true that Manhattan is a big island, but if you have to take mass transit or a cab, take it someplace where you can get out and walk. Take the A train to 190th St. and go for a walk in Fort Tryon Park, where you will find the Cloisters, home of the Met's medieval Europe collection, and great views of the Palisades across the Hudson -- a leafy, undeveloped prospect that might make you forget you are still on the same chunk of land as midtown. You can get the M4 bus back south and see how it all connects above ground.
Or, take the 4, 5, or 6 train to City Hall and walk across the Brooklyn Bridge. At the Brooklyn end, you can just turn around and head back across (you won't be tired of the view yet), or you can extend your walk along the Brooklyn Heights Promenade, which will give you a chance to admire the bridge itself and glimpse the Statue of Liberty and Ellis Island beyond the downtown tip of Manhattan.
But specific destinations aren't the point -- wherever you are, just keep walking. If you are on the Upper East or West Side, Central Park is always an excellent choice; elsewhere, just head away from the center, which we will say is the intersection of 5th Ave and 57th St. if you're uptown and West Broadway and Houston St. if you're down. Face yourself away from either of these points and you are off to a good start.
This doesn't mean that you can?t walk up 5th Ave. past the windows at Sak's, Cartier, and Tiffany, but it does mean don?t stop when you get to the corner of the Park at 59th St. (and don't get into a horse-drawn carriage) -- keep walking. Head into the park or just keep going up 5th. The Conservatory Garden at 105th St. is a good goal for the ambitious, or check out the reservoir at 90th St., or the model boat pond at 74th St., or Bethesda Fountain at the end of the Literary Walk, midpark at 72nd St., or the Central Park Zoo a mere five blocks ahead of you at 64th St. Again, the destination is secondary; the reward is simply to wander through the endlessly shifting scenes that compose New York.