Are museums going to be open for Thanksgiving? I am also interested about renting a car in NYC, but I cannot find anything open that day. Is the airport the only option?
Based on what I can see from the websites the only museum that doesn't explicitly state that they are closed on Thanksgiving Day is NYC Folk Art Museum though it is quite likely that they are.
As far as car rental is concerned the major car rental companies like Avis, Hertz, Budget have offices open on Thanksgiving in NYC but most of their Manhattan locations (if not all) report that they don't have any cars for the Thanksgiving day.
You could try ZipCar but you might have the same luck.