Hi BFLB.
As Lana said, most bars and restaurants do stay open though they are very quiet. There's a nice bar which looks like an English bar on the inside called "The Blue Pine" which is near the American Accademy, thats busy all year round. There's another bar on the Dhekelia Rd called Maximillians which shows alot of English football (6 or 7 games on a Saturday) so if you are a football fan, its probably the best bar in Larnaca for footy. Nice restaurants scattered all over with my personal favourite being "Miligi" on the McKenzie Road who are very generous with their portions and fantastic food. Of course there are loads more, but these are to get you started