New York City
ASan Francisco: Free things to do in San Francisco?
In addition to the other answers, I will suggest the Ferry Building Marketplace. You can browse the stores there, and on Farmers Market days, there are additional vendors. Japan town is also somewhat interesting.
ANew York City: What should be on my "Can't Miss" list on 1st trip to New York City?
Try to go see a Broadway show, although they are not cheap there are ways to get same day tickets more cheaply. For museums, the The Metropolitan Museum of Art is a must, along with the Museum of Modern and Solomon R. Guggenheim...