My family live in Cyprus and there is so much to see. Paphos is definitely focused on tourists and has loads of lovely restaurants, bars, clubs etc. If you want some history visit Limmasol and Kolossi castles. Richard I was married in Limassol castle and he lived at Kolossi. There is a Roman villa at Kourion with an ampithetre at the side. It's really interesting to walk round and in the evening they have plays in the theatre. Nicosia is good to visit. It is the only divided capital city in the world. There is s museum there with loads of info about the 1974 Turkish invasion. A visit up Troodos mountain will show you another side of Cyprus along the way you could stop at Lefkara village and see how they hand make lace.
There really is so much. If you can hire a car while you are there you can see loads. It's only a small island and you can get around easy. Ad the other guys said Famagusta is a good visit as well but can be a bit emotional because of the history.
There's loads of nice beaches Protarus and lady's mile stand out for me.
I hope you have a lovely time. It's my favourite place in the world.