Not a prototypical example of Mongolian cuisine but a cool place nonetheless. The Chez Bernard Cafe serves up Western cuisine and specialises in French pastries (they are very tasty).
It's largely a tourist/expat hangout. It's more expensive than other local restaurants, but then, most other places don't offer fancy cakes and full English breakfasts.
My dining was largely limited to their sweets range, but I also tried their "healthy" breakfast (fruits, yoghurt, and cereal), which was great. The waitresses were all very friendly, and it generally had a nice atmosphere. It looked like a good place to meet people if you're a lonesome traveller.
They also organise expeditions and tours from the cafe.