So much, depends on what you want. Probably cheaper as people said to stay in NJ and take the train in.
I would walk around neighborhoods like Little Italy, Chelsea, Chinatown, Soho and try a fun restaurant and maybe do a tour. There are tons of cheap tours and great ethnic eats. Pizza is delicious in NYC, get a slice at Joe's Pizza (several locations) and walk around Little Italy for a cannoli and stop in Chinatown for dumplings.
Walking across Brooklyn Bridge is beautiful as well.
Here are some walking tours:
https://freetoursbyfoot.com/new-york-tours/