Being American is no special impediment to your safety in Russia - and generally it's pretty safe.... with a few notable exceptions starting with the crazy driving and high road accident rate!
Of course you should stay away from the North Caucuses and the "hot" conflict that's ongoing there. I'd give eastern Ukraine a miss too.
Here's a good article of ours to get you started:
Enjoy the trip
Phil at the safety hub over 6 years ago