Any Greek-Cypriot resteraunt worth its salt will have a variety of meze available to order. Similar to Spanish tapas, meze provides samples of around 15-25 dishes ranging from dips and raw vegetables to fish and meat in richly flavoured sauces.
We found the best place to head for meze were the smaller traditional tavernas, often tucked away down side streets or dark alleys. Instead of ordering from the menu, it is best to ask your waiter his reccomendations, as this way you will be bought out whatever is freshest, tastiest or on special offer that night.
Meze will vary widely from town to town, seafood being more profilic nearer the coast. Among my favourites were the grilled haloumi ( a Cypriot goats cheese) , lountza, another Cypriot speciality made of red-wine marinated pork and dolmades (the stuffed vine leaves one so often finds in Greek restaurants back home).
Try and leave room for dessert if you can. We finished our meze with a sticky honey/nut/dough combination that was to die for (I have no recollection of its name though).