The views may be inspiring. However there are plenty of cons on shooting above the skyline. The first thing that everyone notices while shooting above the skyline is that the glass is going to fuck your shit up. You will encounter these drawbacks while shooting through glass or any kind of window pane for that matter, and you really start to notice it more when you're paying a chunk of change to shoot through that window. Be patient. Take your time.
Moody Weather (This could be good too)
Price of admittance
Most public observatories dislike tripods
Be sure to bring a jacket or something to cover your camera between you and the glass. This will reduce window glare. I also suggest you bring a polarizer (filter) to help reduce window glare. I really haven't found the best solution for shooting through window panes, but these tips seem to at least remedy a significant amount of added glare.
I have found that removing the lens hood and going straight lens to window/glass gives me the best chances of not capturing any added glare/reflections from lights or people from inside the observatories. It also kind of reduces your creativity seeing as you can only shoot straight forward.
Also, no tripods at 360 Chicago (Hancock) and the Skydeck (Sears/Willis/Whatever They Call it Next Tower) I either use a Gorillapod that I bought off Amazon or I use the ground or baseboard at these two locations.
While disappointing to encounter dirty glass on trips to the Skydeck and 360 Chicago I have to remind myself that it is what it is. It rains. So, try to make the best out of bad glass.