Well....can't say much for cleanliness in university men's rooms...I rarely use the restrooms on-campus....but if I do use them, I always use the men's.
The thought of walking into a women's room just gives me an awkward feeling. I do not belong there. (not to mention, living full time, if a single one of my classmates saw me, I'd be a dead man)
I'm not on T yet, but I pass pretty well. If nothing else, I come of neutral, so often people feel like they finally have an answer when I walk into the men's room. (so said a random Homestucker at AWA xD)
But generally the men's rooms anywhere else are just fine. Cleaner actually, mostly because guys don't do much in there. If you feel self conscious, get an stp (you can make one with a medicine spoon that works pretty damn well). It doesn't do anything for you appearance-wise, but it'll make you feel a lot more confident.