*lol* When I read the subject line of this thread, I was thinking: "Does this refer to Domyoji?" haha. I have to admit that I can't think of anyone else like that. (To be honest, I disliked him a lot of the time but yeah, sometimes I loved him.)
The first one who comes to mind is the heroine of Liar Game, even though she's not that kind of stupid. I see you've already watched the first season so maybe you don't agree.
Another one is Gyoten in
Mahoro Ekimae Bangaichi. He's not really like Domyoji, but he's kinda odd, he says things sometimes that makes you go "huh?" and it's a fun drama. (There's no romance.)
The main character of
Umi no ue no shinryoujo is a pretty smart as a doctor, but he's very, very silly and lovably stupid most of the time.
I know, these recommendations are not perfect, but with my limited experience, I feel that Domyoji is one of a kind. ;) But the other day, somebody was saying that Autumn's Concerto is "just as addictive as HYD". I haven't watched it so I don't know in what way they are similar, I'm just passing on the information.