I lived in Nicosia from 1991-1993 and have been back to visit several times.
There are ruins, monasteries, beaches, troodos mountains...that I know of. I think that there are several camp sites but I don't know much about them.
In Cyprus I have been to Paphos, Limassol, Agia Napa, Larnaca, Protaras, Nicosia and Kyrenia and I liked all of them. Not sure what there is to do in any of those cities other than the beach though. I have heard that the Troodos mountains are nice but have not been there.
For transportation I would recommend taking an intercity van. There is a company called Travel & Express that I have used before. They have a bunch of Volkswagen Eurovans and the like and you call them and they pick you up and they go around picking up other people and then they take you to another city and drop you off again. The fares differ by where/to you are going, obviously.
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For me Cyprus is more about sucking up local colour and enjoying the sea. I wish I could be more useful in terms of providing information. If there is anything that I might be able to help with let me know. Hotels in the various cities, etc...
Oh yeah I also recommend going to the Turkish side for a day. It is really easy to get there and it is also much cheaper than the Greek side (by the way Cyprus is pretty expensive). If you do go to the Turkish side, visit Kyrenia (Girne in Turkish). It's a really picturesque town that hasn't been scarred by tourism. There's also a casino there.
PARIS, FRANCE...THE BEIRUT OF EUROPE.