Well, you can probably guess how to get up. You'll probably be taken there eventually, since sometimes patients are left in the chapel up there on weekends. Which must mean you're still pretty new, right?

When they take you up there, you'll pass a few doors until you reach the 'chapel.' It's the fourth one you'll see, I think. After that they'll let you explore the area as you see fit.

There won't be any computers there, but that's all I can tell you about the second floor.

Let me know if you figure out anything interesting about yourself while you're up there.