All of the tourists agencies will tell you some of the basic history and tradition associated with the Old Bridge, but for an in-depth exploration of the architecture, history, and reconstruction of the Old Bridge as well as a look inside the eastern tower, visit the museum!
The museum is one of the best in Mostar, well curated with an introduction to local history as well as detailed exhibits about the museum. The museum exhibits begin in the eastern tower flanking the Old Bridge, so you will get a birds eye view of the bridge below.
You can avoid the netting on the tower windows by aiming your camera lens through the holes - you will get some great photos!