I spent a year researching places to study in Russia after I completed my university degree and I decided on St Petersburg State University. I studied there from Sept 2009-June 2010 and had an amazing time. Not an exaggeration to say it was the best year of my life.

I originally went though the Centre of Russian language and Culture(which they have now merged with the philological faculty's program for foreign students that was also running at the same time. So, they had two very similar programs running out of the same university(just on different campuses)). The prices though universities are much more reasonable than going to a "language school" - they really take you to town - like 1000 dollars a week or something ridiculous like that(whereas I paid 5,0000 for 10 MONTHS).

So basically they have a couple different programs: They have a 10 month long course of intensive Russian language that students take to get to the level they need to enter a Russian University to study with regular Russian people. They have a similar program that is slightly less intensive called "General Russian", 20 hrs a week, which is what I took(you take a test on the first day and they place you in your level and you are free to move up as the months go on and you progress). They also have a special program just for beginners.

I'll just talk generally about my experience: I had a great time and learned a lot there. The classes are 100% in Russian(we started with just grammar, speaking and phonetics classes but as we got better we were given literature, listening, history, Mass media, lexica and film classes as well. Though I heard from friends who arrived not knowing any Russian that the very beginning level has some English just to make sure that everyone is on the same page. So no worries there. Also it is daunting at first but you will be surprised how much you pick up just from listening to Russian for 5 hours a day!(luckily we had class only 4 days a week. Depending on your group you could have any of the weekdays off. I had fridays off for half of my time which was a great, a nice three day weekend which made traveling easier and then later I had Wednesdays off which was a nice little break in the week. The teachers were fantastic, and we were lucky enough to have some stay with us the entire 10 months, and to get fresh blood once in awhile which allowed for some different learning styles, new texbooks/materials as well. At most we had 12 people in a group but most often it was 2-6 people which allowed for a lot of speaking time. And the location is fantastic. It is just absolutely gorgeous in any season. I can't rave about it enough(it was the reason I chose Piter over Moscow. Moscow is amazing, but St. Petersburg makes my soul sing)

Anyhow, here is their new site. Why learn Russian? | The Russian Language and Culture Institute

Other programs which I seriously considered:
1) Russian Language School Enjoy Russian | Petrozavodsk
2) ODESSA LANGUAGE STUDY CENTRE. Russian language courses
3) I also considered going through this place which gives you a huge list of universities to study at in various locations, as well as different programs(just learning language, or culture, fine art, acting, archeology ect.). SRAS Program Search Engine.

If you have any questions feel free to ask!

PS. I know some people have said it is best to know Russian before you go, but I secretly wish I hadn't. I had a lot of mistakes I had to break once I got to Russia. I wasn't taught some phonetical rules during my study of the language at home, and so when I got to Russia it was like trying to re-learn a word with a different pronunciation(Luckily most of us were in the same boat).