One idea: maybe look into apartment swaps or sublets? It might be harder finding somebody who wants to swap for Knoxville (nothing against your lovely town, Dave, just that fewer New Yorkers are likely to be taking trips there than, say, LA, Tokyo, or Buenos Aires) but many people leave town in July/August and need subletters. I can keep my eye peeled on the parents' listserv for my neighborhood if you send me your email address.
As for my recommendations, in no particular order: MoMA, PS1, The High Line, Coney Island, The Cloisters, walking across any of the bridges, The Met, The Museum of Natural History, Film Forum, PS122, Central Park, The Brooklyn Museum, The Brooklyn Botanical Gardens, The Bronx Zoo, Roosevelt Island, WFMU, Governor's Island, Red Hook, The Statue of Liberty, Brooklyn Chinatown, Indian food in Jackson Heights, Chinese food in Flushing, Mexican food in Sunset Park, Carribean food in Midwood, record shopping in Williamsburg/Greenpoint.
