Honestly, if you are only going as far as UB, I would skip Mongolia altogether. The only real reason to go to UB is to eat good Korean food (which you can do much more easily in Korea!) and to get your trip through the countryside organized. There is almost nothing to see in UB itself outside some crumbling Soviet-era buildings (if you've been to any provincial city in the FSU you've already seen exactly the same thing), a temple complex, and a fairly dingy-and-dusty museum.

The real attraction of Mongolia is the countryside. I wouldn't even consider stopping in the country if you can't get out there. Wait until you have more time.

UB is also rather tricky to get in and out of, unless you are in possession of a Chinese or Russian visa. Without those visas, you can reach there from Seoul and (IIRC) Tokyo, but the flights only run on certain days of the week. The runway configuration also makes things tricky if the wind is blowing the wrong way--this happened to me--so you may end up stuck there. This could wreak havoc with a tightly planned itinerary.