Like with many other countries, you can look to your State Department for travel advice for you and your fellow citizens.
In the case of Russia, the US has indeed issued a Travel Alert. It's wise to remember, however, that they tend to be overcautious - if something - anything were to go wrong, and they hadn't alerted the people, there'd be outcry. So even if the chance of problems is tiny, they'll likely issue something.
In this case, some of the key points:
The Department of State alerts U.S. citizens in Russia to the ongoing
tensions in Ukraine and the potential for increased public
demonstrations and anti-American actions in Russia in connection with
Russian actions in the Crimea.
their advice to US citizens:
U.S. citizens considering travel to Russia should evaluate their
personal security situation in light of current political tensions and
the possibility of violence or anti-U.S. actions directed against U.S.
citizens or U.S. interests.
Steps to safeguard one's travel:
We strongly recommend that U.S. citizens traveling to or residing in
Russia enroll in the Department of State’s Smart Traveler Enrollment
Program (STEP). STEP enrollment allows you to receive the
Department’s safety and security updates, and makes it easier for the
nearest U.S. embassy or U.S. consulate to contact you in an emergency.
If you do not have Internet access, enroll directly with the nearest
U.S. embassy or consulate.
Regularly monitor the State Department’s website, where you can find
current Travel Warnings, Travel Alerts, and the Worldwide Caution, and
read the Country Specific Information for the Russian Federation.
But I recommend you read the whole page and based on that, make an informed decision. If it were me, I'd likely still go, but everyone is different in their risk-taking levels.