This place is supposed to be good:
"Secrets Freedom Club: Club and bar located at 67 Artemidos Avenue, Larnaca."
Just go to Larnaca and ask for directions.
In Limassol there is this one:
"Jacare: One of the longest established bars in Limassol situated at 67 Georghiou A' Avenue in the Poppiland Building opposite Dasoudi beach."
Enjoy!