Code Geass R1 and R2 is like Death Note in that it's full of "no, I am the best chessmaster" kind of things that go on. The first season is serious (as in, it doesn't try to make fun of itself, other than that one or two episodes); the second season is nowhere near as serious, but is by far, more entertaining (and more plothax). Both have aired in dubs, already.

Possibly, maybe, Clannad and Clannad: After Story could be up your alley; it might. It's something that the both of you may enjoy watching together. It's a slice of life kind of show, like Bartender, but that's to say, most harems are. It doesn't have quite nearly as much mindscrew, but it's an emotional investment. Also, comedy is bonus points. Clannad has been licensed, but not After Story.

xxxHolic's anime adaptations were also relatively well done. If you like CLAMP, this is the second place to start; it's all of the above at times, but it doesn't score consistently high ranks in your request. The first place to start does not fall under your criteria. The banter between Watanuki and Doumeki is enough to warrant a vouch to any anime fan.