Before deciding whether or not to purchase that flight to UB, consider your tolerance for unconventional toilets and if that's going to affect your ability to have a good time while traveling in Mongolia. Here's my personal opinion/analysis of taking care of "business" in Mongolia.
You have 3 options
Option 1 - "normal" toilet and indoor plumbing just like home but definitely not home. Don't worry, UB (Ulaanbaatar) is fully equipped with these at both guest houses and restaurants. Apparently there are "ger" sub-districts on the periphery of the city and those more than likely have "common" community toilets.
Option 2 - "drop toilet" or a large or (not-so-large) hole in the ground with a wooden 2x floor laid across said hole with the center two 2x's separated by about 12" for you to hover over and hope to God you don't trip into, drop something into, and definitely resist looking down into. If you're lucky, the small wooden shack around the hole WILL have a small knee wall blocking the prying eyes of all those pervy goats and yaks, but WON'T actually have a door sealing you into it the sh*t shack. Between the smell and the flies, the more open-air the better :)
Option 3 - "nature pee" - I think we all know what this one means.
Now that we've defined our 3 options... let's be clear on where you may find these throughout a "budget" or "adventure" tour around Mongolia.
In town/village/ restaurant toilets: Don't be fooled, I use the descriptor "town" very loosely. More often than not it's a village and a very tiny one at that, however I was severely disappointed in large towns as well. Most restaurants have no indoor toilets and still direct you down the street or out back to some of the most disgusting drop toilet around. Often when confronted with this offensive option, we (the group) would overwhelmingly agree to postpone the "in-town" toilet stop for a "nature-pee" pullover option while on the road after lunch.
Motels: This was a new one for me. Apparently, in Mongolia, some people go so far as to build entire buildings (this is already a big deal considering this used to be almost a completely nomadic country where people live in Gers) WITHOUT INDOOR PLUMBING. What?? Clearly this makes no sense at first glance but when you think about the infrastructure required to dispose of human waste, you realize that this really small village you're in doesn't have a waste water treatment plant.... so of course it wouldn't have a sink or a toilet in the motel either. Shocking for 2018. Logical for Mongolia. That said of the 3 motels we stayed in, 2 had a sink and a toilet - one for the whole floor - and no shower. The other one had nada, and see above for "town toilets" so we opted for a location around the corner out of sight.
Tourist Camps: in my mind this was the best of both worlds. Kind of like glamping. You're out in beautiful nature, in a ger most likely with a bed that has a thin but soft-ish mattress, AND a bathhouse! This building contains a sink, toilet, and a shower.... and if you're really lucky, the shower will be hot when you want it too! These camps are basically the hotels of the countryside. They vary in price but the one I went to in Terelj (My Mongolia Eco Ger Camp) was 30 USD for 2 people including breakfast. Quite a good price. I am sure these camps vary in price but clearly you can find affordable ones as well.
Ger Family Stay: while this is the most authentic option, it is another drop toilet situation. That said, because these are families living here, they seem to care a little about their home bathrooms. We even had one family who put down a vinyl floor mat and had incense burning in their bathroom which made it quite tolerable. Fortunately the toilets are dug a pretty good distance from the gers. Unfortunately, at night - because the toilets are dug a pretty good distance from the gers, you may be dodging livestock (I was eye to eye with a yak on more than one occasion) and livestock poo all the way to the bathroom. Such is ... #gerlife.
You are now armed with the full knowledge of the potty situation in Mongolia and can decide if it's still for you!