Good legit massage in that price range is fairly easy to find, but the chances of a young cutie are pretty slim, to none.
For 100% legit Thai massage I'd recommend Ancient Thai Massage on Beverly near Rampart, or Pho Siam, by Echo Park. Both are $40 per hour, as of my last visit. Occasionally there's a younger masseuse who's not so bad looking, but most of these ladies are older pros. If you don't mind the lack of eye candy, the difference in massage quality is worlds above the places with the younger girls who aren't as well trained.
Lately, I've also become a big fan of the foot massage places popping up in the Monterey Park/Alhambra area. $15 for an hour, and most places do a good back and shoulder massage while your feet are soaking. There are tons of them out there, but I usually go to two different places at 250 and 310 W. Valley Blvd. The one at 250 also does body massage for $25 per hour. Great deal, but not the most relaxing spa atmosphere (just some massage tables separated by curtains from the foot massage room.