I can only post about Golomt Bank, as that's the bank where I have my account. My account is a limited account, as I opened it online instead of visiting the bank in person. With a full-featured account, you might have better options, but you will need to physically travel to Mongolia to open one of those.
When you are setting up a term deposit (CD), you have the option to pick the currency: MNT, USD, EUR, CNY, JPY, GBP (see the rates page for rates and fees - click on "Deposit term and condition").
Term deposits cannot be withdrawn until they mature, so you won't be able to change the currency.
Depending on what option you picked when you opened your account, you will either need to travel to Ulaanbaatar to withdraw your funds (which probably means you'll receive Tugrik) or via wire transfer (in which case it will probably be up to your other bank to set the rates on converting to USD).
Which currency you pick really depends on your goals:
If you are looking to maximize your rate of return, you need to consider factors such as inflation rate and exchange rate. Earning 15% on an MNT term deposit won't do you any good if it has less buying power after 12 months!
If you are looking for a hedge against inflation, consider setting up term deposits for multiple currencies.
If you are looking to maintain a financial toehold in Mongolia (in case you might want to travel/move/invest there), local currency is probably the way to go.