However, this was very full the last time I was there so you might have problems getting a space, especially for a long term. Be sure to contact them before you sail towards Cyprus.
The better option in this part of the Med is Turkey which has many marinas with IMHO much better service than western Cyprus. You have Marmaris, Göcek, Fethiye and Kemer all within a day sail of Cyprus.
I am based on Cyprus and have to dissappoint you.
Situation with marinas here is terrible - Larnaca and Limassol are full and you have no chance to arrange a place for a long time.
There is also small marina in Lachi (the most western on Cyprus), which is actually small harbour without much facilities. You may try there. But Turkey is actually better and cheaper. The nearest place to Cyprus is Finikie - I was there 2 weeks ago - plenty of space, all services etc. Or try Kemer, but I have not been there.
Strongly not recommend Fethiye - very dirty place. I left my boat there for 3 weeks and prop and stern fenders were so heavyly fouled that I had to scrab them.
The cheapest place of all will be Yacht Marina in Marmaris - about 250 miles from Cyprus.
problem with Cyprus I hear is that since the war, turbulent times in Lebanon happened more then a year ago, many lebanese have put there yachties over there