I'm not Russian but I've lived most of my life in the USA and still have a foreign accent, and I hate conversations about my country of origin, so I can relate.

I've learned that simply answering truthfully leads to a predictable sequence of annoying follow-up questions I don't want to answer for the 100th time.

No answer is perfect but I've found two patterns that I've tended to rely on over the years:

1. "I grew up in Los Angeles." Now the ball is in their court. Nice people will change subject or ask about LA (what neighborhood, do you know any good restaurants, etc). Rude people will press with something like, "No, where are you really from?" - this person is nosy, so let's have some fun: counter with the non-answer "I moved there when I was very young." ... At this point the persistent ones will switch to, "*No, I mean, where is the accent from?*" - easy answer, "My parents spoke (language) at home... " still giving no conclusive info since many countries speak that language. Try switching the focus back to them with "... how about your parents, are they from here?" or just excuse yourself and move on, this boring conversation has dragged on for long enough.

2. "I'll give you three chances to guess it." Most people will NOT get it right on the first try (i.e. in your case they may pick any other slavic or former USSR country as their initial guess), and if they do, just ask for two more guesses. Here's the trick: start a conversation about each of their guesses. Oh, country X? Beautiful place, nice beaches, bad food. Have you been there? Do you know anyone else from there? This will stretch the conversation long enough that by the time we get to my actual country, it's time to move on.