The city centre around Sükhbaatar Square is walkable, and most of the main museums and the Gandan Monastery are within reasonable distance on foot. Beyond the centre, taxis are the practical option.
Taxis in UB are abundant but unmetered — agree on a price before getting in. Within the city centre, most trips should cost 5,000–15,000 MNT depending on distance. Ride-hailing apps (UBCab and others) make it easier to avoid negotiation. Shared taxis (unofficial, operating like minibuses on fixed routes) are very cheap and used by locals, but require knowing the system.
Public buses cover the city with a rechargeable card system. Routes are in Cyrillic and hard to navigate without the app or local help, but bus fares are low. Traffic in UB is seriously congested during rush hours; walking or cycling (possible in summer) can be faster across the centre than taking a vehicle.