Khustain Nuruu National Park
A beautiful nature preserve. Home to the Takhi (Przewalski's) Horse
Flora and fauna
Takhi Horse and other native steppe species.WikiPedia:Przewalski's Horse.
In winter it is very cold (-30°C) but May through October is pleasant.
Only 100km West of Ulaanbaatar, arrange a tour or hire a car or microbus. Almost all paved road, so it could make a nice trip via bicyle.
There is a fee, about US$10 per person.
Hike, or with a jeep.
There are Gers (Yurts) available for rent and a dining hall.
You may not be able to camp in the park, but you can camp almost anywhere outside. The Tuul river is on the South side of the park.