Perfect Blue is definitely the anime to watch at 3:00 in the morning! @_@
I can't remember much about it, except that I don't know what's real. I think that's intentional, though.
After this we might watch Zetsuai! XD Or Eva. Eva's a good thing to watch in the middle of the night, or early morning, as the case may be.
Koi wa doki doki suru nara...