This week I went around and started familiarizing myself with a great music website called Last.fm. This site is great, because if you go to it (even if you aren't registered), scroll all the way to the bottom, and click on "Weekly Free Download" under the "Top Charts" header, you can find, among other things, Russian music wanting to be downloaded. A lot of it is from the same artist, and it isn't exactly traditional stuff you might expect to hear, but the lyrics are in Russian none the less.
The link for this website is simply http://www.last.fm
If you do decide to get more involved, it's possible to listen to radios of similar artists, and possibly of just russian music, but I personally have not tried it yet, so don't take my word for it. Get in there and try it out!