Spent some time working there in Paphos 10 years ago and liked it so much I went back in holiday with the family. Definitely do the Troodos mountains. The difference in temperature is quite amazing. I went on a jeep safari along the coast and did a tuna fishing trip. Both good. Limassol and Nicosia... not sure, went to a water park in one of them and lost my big toenail on a slide, which was nice, and flew to Jerusalem for a crazy 24 hour day trip from Larnaka. They say Famagusta in the Turkish area is worth a look too.
For food, lots of good places in and around Paphos harbour. IIRC there was a big white restaurant called the Seagull which was good