Would Citibank in Russia count as a US based bank? Also, do you know if I will be able to cash my refund check here in Moscow (in case I pursue check mailing option)?

if it is a Citi bank located in Russia unless it is named an affiliate of the US,  Citi Bank it is not considered  a US based Bank. US Based means that it originated out of and has  been authorized and or licensed  by the US to conduct banking business abroad bearing the US approval stamp. Its just like cashing any other business issued check each state has its rules and regulations but with the proper required matching documents  to confirm identity you should be able to cash your check however you may have to change currency at your expense if its different from US currency again different state/country different requirements,rules,and regulations.

I read that our Citibank is a 100% "daughter" of Citigroup with a foreign capital, BUT is a separate (Russian) legal entity. That corresponds to what you said about our Citibank NOT being a US based bank, right? If not, then only having a check sent to me is an option. Having refund deposited into my friend's account for example would not suffice, right?
Thank you

Question to you if you have an account with CITIBank US, can you deposit into CitiBank Russia account from any US branch ??? 

@fetruche That is a question you should ask your local US based bank.

This is hugely late but as the guy who created Citibank in Moscow, the answer is that there are two ways a bank can operate in a foreign country - as a Branch or as a wholly-owned subsidiary. 

In the case of Russia, the Russian government allowed only wholly-owned subsidiaries because they wanted us to deposit our capital with them rather than rely on our offshore capital which would be the case for a Branch. 

So Citibank T/O was created with $15 Million in capital in 1994. It is now much much bigger of course.