Just got back from 12 days in Russia. Flew into Moscow (4 nights), flew to St. Petersburg (4 nights), overnight train back to Moscow (3 more nights).
I was never stopped for ID, although I wandered all over both places. For the record though - caucasian little-old-lady that mostly doesn't talk in public and tries to dress as native as possible. I did see uniforms all over, but they ignored me.
I used a bus to get from the airport downtown. It seemed fairly logical, and worked well. To get around downtown, it was either walking or the Metro. The Metro sells you tokens which you then use in the machines to enter.
I used ATM machines three times with no problems - once at the airport and twice in Moscow. Took me a while though to figure out that some of the machine were for changing cash, and some were true ATMs.
In St. Petersburg, a very easy excursion is to just catch the boat outside the Hermitage, and go to Peterhof. The boats run every 1/2 hour, the signs are in both Russian and English, the ride is very nice, and Peterhof spectacular.
Do take a little while and see if you can learn a bit of that Russian alphabet, if you don't know it already. 33 letters. Quite a few of them the same as ours (Roman), but about 1/2 of those actually take on a different character. A handful of Greek letters. And the rest are a real challenge. However, with just the Roman and Greek ones sorted out, you will be able to crack quite a few cognates, and it feels so good when you do.
Romelle