Why not just go to a hotel and use their facilities. Princess Hotel on Dekhelia Rd charges non-guests for the use of sunbeds. Thats what I do from time to time if I don't fancy the beach but prefer a swimming pool.
yeh as a kid i prefered swimming pools to the sea. now i rarely go in either. but we used to go the golden bay hotel, they had the best swimming pools. it had slides and a waterfall and stuff. once they asked us to leave as we werent guests, so we just went next door to the next hotel's pool.