South of Λάρνακα you’ll find many nice hotels and apartment houses close to the sea. Especially in off-season you can get good prices here, but you’ll have a reduced amount of touristic infrastructure around you. If you’re hungry or thirsty the Cyprus Fish Tavern at Περβόλια is a traditional place that can rescue you.
It is a classic tavern which serves good fish on a vast terrace which is not located directly at the shore, but you can spot the sea from there. The friendly guys there serve you with Cypriot beer and other drinks. The kitchen closes at 10 pm.
Cyprus Fish Tavern