I asked a related question earlier and got some good answers:
I read a book called Byzantium by Judith Herrin. It was a good and very well written.
"A Short History of Byzantium" by J.J. Norwich is actually pretty good. I haven't read the original version, since I'm from Montréal (I speak french first), but we had to read parts of it in my History of the Byzantine Empire class I took doing my B.A. in history.
It's a good book in my opinion. Of course, if you're looking for some light reading or something, it might not be the best. After all, it's a history book about a 1000 year period... So it's kind of heavy. But like I said, it's a good book.