Basically, don't. I may sound borderline-SJW now but literally everything written about Russians in the West nowadays is exploitation. You can't *not* make him a stereotype, it's ingrained one way or another in why you want to write him as Russian at all. It shows in your very expectation to receive a coherent answer about "how to write a non-stereotyped Russian character" without specifying anything except that he's male and "un-Americanised".
You may think all you need is a comprehensive enough "list of cliches to avoid" (and of neutral trivia to write in for authenticity), but it doesn't work that way. A large part of the stereotyping of Russians, and perhaps the most harmful part, is not the repeating of old cliches but the ease with which you can make up as you go along, and expect to be believed. The real problem is that a lot of people would believe the most outlandish things when they're said about Russians. Anything that is "different" or "cultural" enough will "work" in a Western narrative about Russians, which means that the list runs forever. The basis for stereotyping Russians is summed up in that rather intellectually lazy "riddle wrapped in a mystery" quote by Churchill. In practice, "riddle wrapped in a mystery" means "anything goes".
Just to name a particularly grievous example: the game of "Russian roulette" was entirely invented in a work of fiction (a 1937 short story by George Surdez), and most people nowadays seem convinced that this disturbing idea has some obscure roots in actual Russian history. That's what makes it impossible to just give you a list of things to avoid. We can never know what you guys will come up with next, but we can be sure that whatever it is, however wild it is, most of your readership will believe you're describing us actual Russians. Not to mention that a lot of those complete inventions aren't far-fetched but the opposite, insidiously quasi-realistic.
Just don't. Unlike most other much-stereotyped groups (who I'm ready to admit are impacted much harder by it, or at least much more directly), we're generally fine not being "represented". Just being absent from Western narratives, until the cultural fog begins to clear, is better than another exercise in reinventing a Russian even if it ends up with less stereotypes or random inventions than average.
Write it and give us a link to it. If there's something too wrong about your character, we'll tell you. But keep in mind that all people are different, Russians included, so there's a huge variety of personalities that will pass for 'proper' Russians.
if you know nothing about Russian people, I doubt, it is a good idea to make Russian person your main character. Culture of any country is not something one can explain in 10 lines. Especially since you don't specify what kind of person it will be (education level, age, ethnic origin, profession, time spent in USA, reason, why person moved to USA etc...).
"what is considered "morally right" for example" - approximately the same as in any European culture.
"A lot of different ways of thinking or even acting can be influenced by your own cultural norms." - there are millions of situations in life. Is person dating? is he getting married? Is he on funerals? At work? At school with his kid? Talks to someone on certain subjects? On the beach? in the store? At the restaurant? etc...
A character doesn't depends on culture. But differences can be in action and thought and need to examine each situation individually.
I know that but different people might have different opinions on what is considered "morally right" for example, depending on what their individual cultural norms are. A lot of different ways of thinking or even acting can be influenced by your own cultural norms.
