what about Chiyono on east 6th st (along Curry Row). A set menu with a bunch of choices and "course" is $20-$30, but you can order dishes separately (mains are about ~$15 I think). I thought the omakase set was pretty good and interesting there.
Otherwise, I've not been but Cha'An teahouse may have similar food. It is also nearby, on 9th St, I think.