Syria is great. People are friendly, the sites are amazing, food is good. Damascus is wonderful. The trucks and buses try to run you off the road but that's not unique to Syria. Border officials are helpful and are not corrupt. The place is relatively safe. I was followed by officials in a Land Cruiser for the first hundred kms from the Turkish border (I had to keep slowing to let them catch up!). They left me when I entered the sheep country on the Iraq side of the main eastern higway to Palmyra (about 10 minutes before I got myself lost and had to camp with a shepherd's camp before it got dark and I ran out of fuel). The north-west of the country is beautiful with lots of castles and ruins, but the crossing into Lebanon here is a nightmare (and I think it is presently closed).
Lebanon is a beautiful and interesting place. The drivers are all mad and very aggressive, and bikes are treated as mobile chicanes. I was hit twice in one day! Definitely worth it if but ride defensively. Borders are mayhem and the insurance touts work with the customs officials to rip you off. Best stay away from the northern Palestinian areas - they are being shelled by the Lebanese army. I think the northern border is closed at the moment. The main northern highway runs right past the worst of these areas so you don't want to enter Lebanon from the north anyway. There are sporadic demonstrations in the Christian areas east of Beirut. The highway to the main border crossing runs through these areas so check before leaving Beirut for Damascus. The south is still war-ravaged but there are some lovely towns down there along the coast. The Bekaar Valley is particularly grim, especially in the south, after the Israelis caned it. Virtually every bridge was bombed and hadn't been reparied when I was there in December last year, made for a slow trip. Domestic politics in Lebanon seems to be getting worse by the day - so check where the hotspots are before going.
Jordan is a piece of cake. Beautiful country and wonderful people. Highways are good and the off-roading is amazing. This is one place where fuel can be hard to find so be sure to fill up whenever you can. You can buy fuel using just about any currency, so it's a good place to get rid of the leftover money from other countries.
Israel is fabulous with some great motorcycle roads, especially in the north. There are other bikes in this country so the drivers are a bit more aware (though still pretty aggressive). Very safe country. Some of the best places are the big Palestinian towns (Nazareth was my favourite) although hard to beat Jerusalem (parking the bike outside a 900 year-old pub in the Armenian Quarter and sampling Armenian cognac - they reckon they invented it - but then I could go on all day with Israel stories). Rockets are falling in the towns near Gaza but you'd have to be unlucky to get nailed by one. Be sure to go to Israel after Syria and Lebanon. Jordan is no drama after Israel.
Stay out of Gaza - the Israelis are shelling hard at the moment in response to the rocket attacks. Not sure you can get in and out of the place anyway. The West Bank is safer but you might find yourself isolated. The borders close regularly and you might get stuck on the wrong side. Many towns are quite hostile to foreigners and you will have kids throwing stones - aiming to hurt. Something striking about the place is the way all kids play war games. Never football or basketball or other runaround games. It takes a while to notice but when you do it's quite chilling. There isn't a lot of joy in the place and it's quite neglected but there are some beautiful spots. Getting in is relatively easy, usually just a passport will do (I guess it depends where you come from). Getting back into Israel much less so. If you intend to go there make sure the Israelis know exactly where and when you are going (and, needless to say, your own embassy) so they are prepared to let you back in. The East Jerusalem crossing on the road to Ramallah is best. Most of the western embassies are in Ramallah and should help you if you get in strife. Be aware this can be a dangerous place and all countries recommend their citizens stay away. Hamas and Fatah are shooting at each other at the moment and it usually pays to stay away from countries where there is a lot of shooting. Check before going in and if there is trouble stay away. If you are slightly nervous stay away. Check with the Israeli embassy in your home city to check their current policy on border crossing as it is reviewed daily. There are lots of NGOs operating in the West Bank and these might be a good start for info on accommodation - although in and out in one day was my preferred option.