I've only been to a couple izakayas. I know one in Little Tokyo, can't remember the name right now, it's like in the 3rd or 4th floor of this shopping complex. It was like 10 bucks or less for most things I think. I'm a cheap college student, so I usually stick to beer and one of those cheap plate things for like 3 or 5 bucks. I could ask around for more places if you guys want. Or maybe some people here already know a place nearby.
And they have a karaoke place in the same building. There it depends on how many people go. But I don't think I've ever spent more than 20 bucks on karaoke, and I've spent hours in those boxes. And yeah, I'm talking about karaoke boxes and not bars, where you go into a room. So you'll be only among friends, with many who probably can't sing for shit anyways. Karaoke is an awesome way to just have fun with friends.