One of the easier Mongolia sites with a bus going daily from UB and it "only" takes most of the day with lunch break. The main reason would be to visiting Karakorum's Erdene Zuu. The town is small and was the capital of the Mongol Empire for only a short time. One often thinks of the Mongol Empire as a huuuuuge place but people were scarce and if they would join the empire it's mainly because "woah this guy has a horse" and they never see him again. Well you might giggle now but this wasn't exactly Alexander the Great conquesting the area. With the monastery gone (it's an hour visit tops and right in town) you can arrange for your hotel/homestay to go visit the locals. Anything will do because you basically "ticked off" the site with the monastery but it would be nice if you go for something nice, like local yurts and their horses. The valley is large and empty so I suggest you spend a few days here. The only hotel they have is nice but quoted a huge sum (are we still in Mongolia??) so the local places are the way to go, plus they will help you visit locals more and you get to meet other travels.