So far I've visited three - Jordan, Egypt and Libya.
Jordan is great for a small country - so much varied history, scenery and culture - and quite peaceful too. I only spent a week there, but I've already written two hubs about Jordan's historic sites, and a third is on its way. I would probably choose it as my favourite, though two weeks is probably enough to see everything of real interest.
Egypt of course has the greatest attractions of all, (especially the pyramids and Abu Simbel Temple), and sailing down the Nile is one of the world's great experiences.
As for Libya - I went there for just 2 or 3 days to see a total eclipse a few years back. Miles and miles of desert and not much else inland, but there are some spectacular Roman ruins near the coast. Didn't have much communication with the locals (especially the women who were largely hidden away), but the people I saw were friendly and quite curious about tourists. However, I'm not sure I would advise visiting Libya at the moment!!!! (Unless you pack a suit of armour in your luggage).