BF and I tried this place, local to us, on Sunday night.. . we'd both go back. I'd also put it quite a bit higher in the rankings than Mo's for that kind of food, though BF said about the same level.
Burger Meister advertises all Niman Ranch beef; their website had listed a hot dog, which was then not on the menu board when we got there. I asked about it and the server said they'd taken it down because they had just changed vendors and the hot dog was now someone else's -- not Niman. Can't remember what it was, but it was delicious. Split down the middle and grilled face-down, a foot long, put on a long french roll to serve with good (basic, frozen) fries. French roll was far superior to most blah hot dog buns. Around $6.95 including fries (but overall it seemed cheaper than Taylor's Refresher, which has similar focus). Fountain drinks have free refills. Beers are cheap during happy hour, from 4-7 pm. BF had the cheddar-avocado burger, which was cooked to order a true medium rare (and even on the rare side).
Lots of condiments out and available. Tiny place. You order at one counter and then can eat at various other counters -- about 12 seats total in the place.
I want to go back to try the fish & chips and some of the burgers . . . .
759 Columbus Ave. (at Greenwich)