If you're into more recent art the Museum of Modern Art in Prague is a definite must-see. The cubist museum is also excellent, I agree. For my money the best "musuem" in Prague isn't really a musuem - it's the Obecni Dum, a suberp Art Nouveau building, the tour of which will blow your socks off. They also have pretty damn good exhibitions there on a regular basis.
As far as Cyprus is concerned, it's not an art gallery/museum -ish kind of country, as most of its antiquities and cultural heritage are all around you; however, I'd recommend as must-sees the Pafos mosaics and the Kourion archaeological site. There are one or two fairly interesting museums in Nicosia - The Leventis and the Hadjigeorgiou Mansion spring to mind - but probably not worth making a special journey for. Nicosia is, frankly, not a particularly pleasant city, especially in the summer heat.