Chobits is nice. It has a bit of fanservice in it, but I really liked it in spite of normally hating fan service. It also explores a theme that I find very interesting and wish more works of fiction should.

ALso, Nichijou is just absolutely hilarious and you have to watch it. No excuses. Just do. After that, try Arakawa under the Brigde. You need to see this, shion. Trust me.