If you have a stack of rubles on you and you're not sure how much they are worth, there is a website that can help out. XE Universal Currency Converter (see Resources) gives up-to-date conversions for just about all monetary units used throughout the world. Select "Russia Rubles" in the "From this currency" queue and type in the amount of rubles you have. In "To this currency," select "United States Dollars." Click "Go" and the site will convert the amount.
If you know you're going to have an ample supply of rubles before returning to the United States, stop by a local money changer and convert the money there. He will most likely give better rates than you'll get once back home.
If you return to the United States and still have that pocket bursting with rubles, stop by one of the money converter stations in the airport. You won't get rates as good as those back in Russia, however, and you'll most likely be stuck with the coins.
So let's say you are back in the States and didn't realize you had extra rubles in your suitcase until a month or so later. It will be a little more difficult to exchange the money because not all banks in the United States convert rubles to dollars. In fact, very few do. Your best bet will be to call your bank and ask if it provides foreign exchange. If not, chances are a banker will point you in the direction of one that does. You might have to do some driving, especially if you live in a smaller town.