Take a look at the tiny, hole-in-the-wall Burmese restaurant at the VS Guesthouse.
36 Khaosan Road,
Bangkok 10200, Thailand
Turn onto Khaosan Road and take the first right into the small alley. Keep walking until you see the VS Guesthouse. You'll see a tiny restaurant with indoor and outdoor seating.
Dorm beds - 120 baht / Single rooms - 200 baht.
I have no idea about the quality of the rooms but I'm assuming they're bare-bones.
However, if you want authentic, inexpensive Burmese food, give the place a try.