I mostly watch slice of life stuff. K-On, Lucky Star that kind of thing (yes I love Nichijou too) but I'm also a big fan of magical girl series like Illya/Fate, Sailor Moon, Cardcaptor, Madoka, etc. I generally don't like sci-fi or horror anime; which is weird in terms of horror at least because it's probably my favourite genre when it comes to live action films. It just rarely seems to work for me in anime, or animation generally. I love the whole kawaii thing which obviously isn't that compatible with horror.
Have you watched K-On? As a J-Pop fan I can see you liking that. And it's just a great series all-round.
https://www.youtube.com/watch?v=TIpA_B5khZc