Frankfurt has a ton of museums if you're into that sort of thing. The Stadel art museum (Stadelsches Kunstinstitut und Stadtische Galerie) holds major art collections, and the film museum is interesting (Deutsches Filmmuseum). The film one is more centrally located on the south side of the river. The Stadal is further out from the centre (if I'm remembering it right it's over on the eastern side of the city).
There's also the Main Tower, one of the tallest buildings, where you can take a lift/elevator to the top and see a 360 degree view of the city. If it's clear weather it's good at night too with all the city lights. Enterance fee used to be 4,60 euros.
