Beirut is fun! And if you are considering the Levant it avoids the awkwardness of Israel. Cyprus would be the easy option, but a very comfortable one with lots of options open beyond Ayia Napa .

Though Oman still fits your requirements quite well. As for the booze question, I've had enormous fun at busy alcohol-free restaurants (YMMV, of course!), and drinks are certainly served at restaurants and bars attached to the larger hotels.

It's not a a single-destination place: Nizwa is most certainly worth an overnight trip; Salalah is an hour's flight south, but fascinating; and the separated bit of Oman that is Musandam on the straights of Hormuz is breathtaking.