For a one-day visit, I'd stick to 42nd St. and north. Even going to the Empire State Building and Macy's (34th) is a detour; going to lower Manhattan (Battery Park, Wall Street, Ground Zero), on tourist bus, subway or otherwise, will eat up a lot of time.
Do Top of the Rock in lieu of the Empire State Building. See the tree at Rock Center. Wander around Times Square and up Broadway to the Ed Sullivan Theater (where the Letterman show is). Eat at Carnegie Deli (share one sandwich and order extra bread). Go to the Museum of Modern Art (MoMA) if you wish to see the famous Picassos and such. Wander 5th Ave from 42nd Street (the Library, and Bryant Park behind it) north to the Plaza (59th Street). Consider an expensive carriage ride through the south portion of the Park. Better yet, enter the Park at 59th Street, walk past the pond, the Wollman Rink, then along the East side of the Park through the Zoo (not expensive, go ahead and visit the penguins), past the Children's Zoo and the statue of Balto, veer left up the hill and down the Mall, down the steps to Bethesda Fountain, perhaps a detour West to the Bow Bridge, then back East past the Loeb Boathouse to the Conservancy Water, then North to the Metropolitan Museum. Go the Met and see at least the famous Impressionists and 20th Century collection, then across to the other end of the Museum to see the American Wing and the Temple of Dendur. Catch a cab across the Park to the area around Columbus Ave and 80th and find a place to eat there on the West Side. Then walk over to Zabars on Broadway and buy a chocolate babka, or pick up bagels at H&H practically next door. Take a cab down Broadway back to midtown, past Lincoln Center.
A more adventurous itinerary? Start with Salami and Eggs at Katz' Deli on the Lower East Side. Walk to the Lower East Side Tenement Museum and take a tour. Walk a few blocks to Little Italy, then down through Chinatown and the legal district to City Hall. Walk out onto the walkway on the Brooklyn Bridge, at least to the first pier, and take in the view up and down the East River. Walk back and peek into the lobby of the Woolworth Building. Continue a few blocks to Ground Zero, then a couple more blocks to Trinity Church at the head of Wall Street. Walk down Wall Street and try to get tickets to the gallery at the New York Stock Exchange (assuming it's a trading day). If you still have any energy and time left, continue to the Battery.
