Yeah, Statue of Liberty is a must-see, and we'd better hit that up as soon as possible, because in the summer it's crawling with tourists. Grand Central's easily done, unless you're into architecture, in which case Annabeth would be a better guide because she knows everything there is to know about the design, structure and construction of the place.
The Fish Market wants to be Pike Place, but it's worth checking out if you like that kind of thing.
You should also see the Empire State Building, even if it doesn't go up to Olympus anymore.