Making your way around Ulaanbaaatar isn’t really a problem- you have plenty of options. Buses as well as trolley buses run throughout the city, but travel on these only if you’re used to crowds, and don’t mind having the breath squeezed out of you- they tend to be notoriously overcrowded. Some private operators run minibuses along the same routes as the actual buses, and these are usually less crowded.

If you’d like to rent a car and this is a comfortable and convenient option, travel agents and hotels are good people to contact for assistance. Alternatively, you could use taxis- many of them don’t have meters, and you should try to get a fix on how much you’ll have to pay, before you get in. An unusual thing about Ulaanbaaatar is that almost every car on the street is a potential taxi - if you’re stuck, you can actually hail a passing car, and get dropped to wherever it’s convenient, at approximately the same price as what you’d pay for a taxi. Don’t attempt it late at night, or if you’re a single woman, though.