The Jezira is a large area and the sights are rather spread out. Visiting them all takes a good 4 to 5 days, but those would be long days. Even if you don't have the time to spend, you can still see the major sights.
Rasafeh: Probably the best ruins along the Euphrates. The dramatic desert setting makes them even more impressive.
Deir ez-Zor: Easily the best town in the region. With an attractive setting, a nice atmosphere, and a great museum, Deir ez-Zor is the perfect base.
Dura Europos: Another set of amazing ruins whose spectacular setting on the edge of the Euphrates is a breathtaking sight.
Other than those there is the culturally interesting Kurdush and Armenian town of
Qamishle on the Turkish border that makes for a great stop for a night.
Quick Tips:
As I said, things are very spread out, so try and make a plan of what you want to do. Know what you want to see, but don't get too ambitious.
In the summer the heat is terrible, but in the later months it is quite nice. Still, many of these sights are in the middle of nowhere with few places to find shade and water so always make sure to have plenty of water, a hat, and some sunscreen if you burn easy. The desert sun is strong.
Best Way To Get Around:
Easily the best and easiest way to get around is by renting a car. This can be done in Damascus, Aleppo, or Deir ez-Zor. The sights are very hard to get to and it can be a bit frustrating relying on local transport. With your own car you will be able to see the most in the shortest amount of time.
However, part of the fun for me was the local trasport. I had some great experiences hitching rides and catching mini-buses. If you are adventurous and have the time, it can be a lot of fun.