Nicosia is a good day trip and you also now have the benefit of being able to cross over to the north at the checkpoint on Ledra Street.
If you are travelling from Paphos you can also take the coastal road for part of the trip back and take in Kourion and also Petra tou Roumio (Aphrodites birthplace) on the way back.

You'll probably find you can book a trip via your rep, but it's easy enough to drive if you want to hire a car.

Dave

Go beyond Troodos. Kakopetria is well worth the trip.

Lofou.

Kykkou Monastery.

Lady's Mile Beach, Kourion and the Temple of Apollo.