yes
just take your driving license with you
the trudos mountains is worth driving up to but dont tell em your russian when u get near the military base :p
dont drive over to the turkish side of cyprus as you wont be insured and the turks will set fire to it
go to nicosia [old town] and try eating in one of the restaurants near the border [food is beautiful]
if you want night life then paphos and ayia napa are either end of the island - u also got a stretch of clubs in limassol
very expensive place atm and expect to pay silly money for branded beer & alcohol
and before you ask i am half cypriot [greek]
pane gamisou pushti = good swear word