Inside you have to assault everything that Moves. As an Instance, the Shivas and Mutants doesn't respawn, but the blight wolfes will come every 30 seconds with a new respawn at the same area. They are not that hard, but they respawn so fast, that you could walk nowhere without some of them.
On the left side at the second floor you found the Dusty Chest. On the right side, first and second floor you will find a curious debris. To go at the second floor, you have to enter the Building and go right. The second door on the right side is signed with "stairs". The metal stairways doesn't conveys you to the second floor.
The Bosses for the Mission you find also on the right side at the large Room, you reach over the metal stairways. The doors beneath are blocked.
To reach the Dusty Chest gives you the Achievement UrbExer: New Flagstaff U. and is part of the Achievemt: Urban Explorer: Northfields.
UrbExer : New Flagstaff University
Find the cache in the New Flagstaff University
Kill Professor Eddings at New Flagstaff University.