I'm going to be giving an informal presentation on this event by the end of this month and could use some recommendations. I've got a biography on Constantine XI and Mehmed II along with some general reading on the Byzantine Empire and it's decline but none of these works so far provide an in-depth, retrospective account of the battle itself from both sides in terms of tactics, equipment fielded by respective armies and the general progression of the siege. I know mainly how it started and ended, but not the in between.
For your purposes, Osprey's Constantinople 1453 may well suffice.
http://www.ospreypublishing.com/store/Constantinople-1453_9781841760919
For a longer text narrative, I suggest Roger Crowley's 1453
I would say Steven Runciman, The fall of Constantinople 1453 (Cambridge 1965) is still one of the best books on the topic.
We have some great articles on this over at r/Byzantium.