If you only have four days then you'd be looking at the east coast or maybe somewhere like Chicago.

Washington DC is a great city, lots of museums, the National Mall, Arlington National Cemetery and very close to NYC if you wanted to take the train there for example.

Chicago has Lake Michigan, the Willis Tower, the John Hancock Tower, pizza, Goose Island Brewery, Navy Pier and so on. Again, a real variety of things to see and do.