Sometime before Christmas I read Anne Perry's The Sheen on the Silk, a novel about Constantinople after the sack. I'd read many of her mystery novels.
Which led me to the history I finished reading about three weeks ago that I started on New Year's, The Fourth Crusade: The Conquest of Constantinople, from my brother's library. The book had a lamentable lack of a good map of Constantinople that was remedied by a reference to Wikipedia: Constantinople.
He also has the trilogy of the history of Byzantium by Julian Norwich, which I will read as time allows after he drops them by.
Commenters at Amazon say that Warren Treadgold is a readable historian who pursues more of the cultural aspects of Byzantium.
As a separate offshoot, Charles has a couple of books on the history of Venice.