Oh God, Oblivion, you'll be fine, especially if you stay in Manhattan, doing regular touristy stuff. Don't be a pansy. New Yorkers are pretty helpful, even though we are known to be rude.
Do's: Have fun, eat great food, go to shows if that's you thing, visit the museums and parks, go on the Staten Island Ferry, visit Ground Zero, check out the farmer's market at Union Square, cross the Brooklyn Bridge, explore Brooklyn--DUMBO, Williamsburg, and Greenpoint have some great stuff, try to catch a game in one of the new baseball stadiums, go to Ziegfield's for a movie, enjoy the nightlife, use the the subway.
Don't: Stand in the middle of the sidewallk to take pictures, move to the side. Don't give panhandler's money. Don't be afraid to ask for directions.