Cyprus

It all depends on your personal likes and dislikes. If it was me I'd pack a phrase book, grab a bus to somewhere ( anywhere )and when I hit a small out of the way town that looked interesting I'd get off, find a bar, have whatever the locals were drinking, ask if there were any rooms to be had for a couple of nights, explore the town, eat local food, get a tan, re-read Raymond Chandler's 'The Long Goodbye' for the millionth time, pick fresh oranges, eat local olives, go back to the bar and chat with the Cypriots, walk home under the stars and do it all again the next day. My youngest son, on the other hand, would hit the beach, chase girls, not come out of night clubs until dawn, drink beer for breakfast and have a holiday romance with a Dutch girl.

It's your three days and whatever you want to do can be done.

depends

anywhere the locals are friendly

eat soufla, mezze, and fish
with the local beer KEO
taste haloumi and olives on charcol
ouzo comes in six ounce bottles ice cold
in an authentic cafe or taverna
and hard liquor comes in small bottles too
try a coffee, medium, or sweet

if you have a car
visit paphos, the monastery
or go north, right to the tip
it takes one day.

in Larnaca
where you arrive
its fun, and visit its
older areas
but Cyprus has tastes for
everyone.

Well, the question is kind of general... i am from Cyprus and i can give you tips but i need to know more about your interests... I would not take the bus as the friend from the UK suggested, as there may be villages that have no rooms or bars...:)
The weather may still be good for the beach and the ancient sites are probably a must...
i second the halloumi, make sure you try it grilled as well...
email me for more info...