.... it depends on how "rustic" you want the food to taste.
Beef stroganoff is like a stew, correct, poured over noodles?
If you want to stay true to its Eastern European (or inspired E. Euro) origins, stick with vegetables that you find in that region. I imagine Brussels Sprouts, cabbage or a green bean would be good. A cucumber salad, made with sour cream, sugar and vinegar would also match. If you or any of your guests are prone to flatulence, be mindful of stuff like cabbage or cucumbers.
Also, if you actually were in Russia, your side dishes might be something like beets and/or peas in a sweet mayonnaise sauce ... some of these foods are not well-adjusted for American tastes.
If you are doing some kind of west-coast fusion kind of thing, you can try something more daring like bok choy.
A green salad is good for an all-american contrast. You can't go wrong with that.
It all depends on the crowd.