Unfortunatley even though Sarajevo is internationally recognized hub of great artists and artistic expression, it is poorly organized and funded by the state. Most of what is done in Sarajevo today is done by the artists and through international donations. The Sarajevo Historical museum has fallen into disrepair but still houses one of the most important exhibits in Bosnia today "Sarajevo survival tools" a great museum that takes you inside the Siege of Sarajevo and daily life in the city.
I saw the Ron Haviv exhibit here "Blood and Honey". I also saw this in an exhibition in Dubrovnik. I don't know if you can still see that exhibition, if you can it is a must see for anyone interested in the wars in Yugoslavia. His photographs from 1992 are some of the best from the entire war.
The people running the exhibit are very friendly and helpful.
A link to their virtual website
Also the UN reports on the shelling and sniping in the Siege of Sarajevo