the best way to watch Code Geass is watch R1, then skip to the end of the last episode of R2. it won't make a lot of sense but it'll be a lot more enjoyable.
Cowboy Bebop, Samurai Champloo, and Space Dandy are all directed by the same guy. I haven't seen Samurai Champloo but I've heard it's good. Space Dandy differs from the first two since it's mostly comedy.
Gungrave is pretty good, I second that recommendation.
Try Darker than Black. Don't watch the second season though.
Or he could just watch it himself and decide whether or not he likes it instead of you deciding for him. :/
One Piece <-- Fun and outrageous!
Hunter x Hunter <-- Also fun!
Gurren Lagann <-- Hilarious and almost as outrageous as One Piece.
Macross Frontier <-- Epic mech battles!
Suisei no Gargantia <-- Really touching story on several levels, probably the best post-apocalyptic anime I've seen. Didn't want it to end.
Kore wa Zombie Desu Ka <-- An... interesting story about a magical girl zombie boy... Yeah, just watch it, lol.
I think Accel World has to do with an MMO, not entirely sure.