According to Wikipedia, "the Trans-Mongolian Railway follows an ancient tea-caravan route from China to Russia and connects Ulan-Ude, on the Trans-Baikal (Trans-Siberian) railway in Russia, with the Chinese city of Jining, by way of Ulaanbaatar in Mongolia." Lots of tourists pass through Ulaanbaatar each summer, and some don't venture far from the train station. With them in mind, I've placed a cache that is a quick and easy grab, even if you're in town for only a few minutes.
The cache container is a magnetic keyholder, which is starting with a log, Mongolian flag pin, and a couple of coins. BYOP. It is hidden on an "L" Series Steam Locomotive. Beginning in 1949, twelve locomotives of this series began working on the Ulaanbaatar Railroad. This locomotive was put on permanent display as part of the 65th anniversary celebration of the railroad.
You shouldn't have to be super-stealthy, but there are a lot of muggles around, so use your head when hunting for, retrieving and replacing the cache.