Visited St. Petersberg and Moscow about 10 years ago. My impressions then were that Russia was a place of extremes. Extreme wealth and extreme poverty. Especially in Moscow.
I really liked St. Petersberg, thought it was a beautiful place. Moscow on the other hand felt edgier... don't know how else to describe it. Many of the buildings felt a bit old inside, decor from the 60s and 70s etc, though everywhere was clean and well maintained. I'm told by a Russian friend that much of the area around red square where we stayed has now been re-developed and is much more modern. In terms of the history and the buildings etc. though it's an amazing place.
In terms of the people, well it was only a 2 week trip, but basically I found them to be typically Russian! Many people seemed.. depressed, but then you realise it's just their demeanour, you certainly don't get bouncy enthusiasm or people springing to help you, but then some there still live in 60s communist concrete high rises, earning just enough to live on, while watching others amass fortunes so large they can easily buy small countries. Never seen so many clapped out ladas driving alongside limos / top end Mercedes etc.
It's a wonderful country to visit, however my suggestion would be to go as a tour group or at least with a few people rather than on your own. I don't think many native Russians would be hurt if I said that crime (pick-pocketing, gang related stuff etc) is pretty rife, especially in Moscow. As a group of 20, 5 people had their pockets picked while on the tram system alone! t's all down to that massive social divide.
Now I'm sure things have moved on in the last decade, and i really don't want to put you off. It's an amazing country with some extraordinary buildings and perhaps one of the most interesting and most colourful histories of any large human civilization. If you can g, you definitely should, know I'll be heading back as soon as I stop being a student and actually get myself a pay cheque!