I've spent something like 12-18 months in Mongolia, mostly during the summers.
It's pretty amazing and keeps getting better. Great restaurants, internet is fast and getting more and more stable. Data plans are cheap and very reliable. Electricity goes out less and less. Only thing that's annoying is that, incredibly, they still turn off the hot water for a few weeks every summer.
Ulaanbaatar is a bit more expensive than other Asian cities. Rent is between 400 and 1000€ for a normal apartment studio or 1BR apartment. Food is around 10€/meal (including drinks -- unless you eat Mongol food, but many people don't and it's impossible if you're vegetarian). Taxis are cheap.
You'll get a 3 month visa on arrival as an American, but if you're European you'll only get 1 month per entry and can extend for another month once every 6 months. If you stay longer and have to do visa runs it can be pretty expensive. Return flights to Korea are around 600€, to Beijing 400-500€ plus you have to get a visa. Most countries can only apply for Russian visas from their home country. The cheapest option is to take the overnight train and do a Thailand/Myanmar-style visarun to China at Erlian for around 50-100€, but it's a real pain in the ass as you have to apply for a Chinese visa and have to sleep in a train for 2 nights and be in transit for a day (I did it a few times. I'm not very social and tend to dislike the trains. Then I started bribing the conductor and getting a private cabin in the personell wagon).
If you want to go to Mongolia, the summer of 2016 is a great time to do so. Travel is incredibly cheap this year because of the ASEM summit. I saw Frankfurt - UB for as cheap as 350€ (normally more like 750€) and there are rumors that they'll lighten the visa requirements too.
Edit: almost forgot: the Mongols are great people, very relatable. The Koreans say about the Mongols that they have an 'Asian face, Western mind'. It'll be very different than places like Thailand where you'll hardly have real contact with locals. The only thing that's incredibly sad is that due to the current economic crisis, everyone is broke right now (while maybe 5% of the population is incredibly rich and very eager to show you their wealth).