Learn the language.
Don’t travel to Russia knowing no Russian.
At least learn the Cyrillic Alphabet so that you will be able to read signs and find places of interest. Learn how to say a few basic words. You’ll feel less like a tourist if you’ve taken the time to learn a few basic phrases. There are some great apps such as Reverso to help you.
Don’t expect Russians to understand English, especially in Moscow. I’m not sure if they aren’t a little like Parisians where they deliberately don’t understand you, or if they truly know no English words at all. You’ll have to learn some Russian if you want to be understood.
I know it sounds weird, but if you smile at a stranger, most Russians will think you are crazy. And don’t expect service with a smile. Your waitress won’t grace your table with anything but the food she’s serving.
You may think she’d being rude, but this is just the Russian culture. They don’t smile until they get to know you and make friends with you. Then they’ll laugh!
Do eat the local cuisine.
Russian food is hearty and delicious. Lots of soups and stews and casseroles that will fill you and warm you up. And not too expensive either. Try a local delicacy. The Czar’s Salmon Soup in Saint Petersburg and the Moscow cake in Moscow are two I can recommend.
Don’t use taxis.
It’s better, safer and much cheaper to use Bolt https://bolt.eu/en/ in Saint Petersburg. It works like Uber so you don’t have to carry cash. You will receive an email immediately detailing your trip and the charge. Bolt hasn’t yet arrived in Moscow, but they do have an Uber alternative, Yandex.Taxi. https://taxi.yandex.ru/ It’s cheap but has the disadvantage of needing to be paid in cash.
Do your research thoroughly.
Research the places you want to visit. Find their actual website and don’t rely on such sites as Trip Advisor for accurate advice. Check for opening and closing times, seasonal variations, and don’t assume anything.
Just because it’s common practice for museums to be closed on Mondays all over the world, don’t think Moscow will be the same. They close on Thursdays! I was so disappointed I missed visiting the Kremlin because of this variation.
Catch the overnight train from Saint Petersburg to Moscow.
You will save on a night’s accommodation and will have the whole day to explore. I caught the day train thinking I would see the countryside, but there’s really nothing to see. http://www.russiantrains.com/
In Saint Petersburg, stay anywhere on the Nevsky Prospekt to access all public transport- buses and metro as well as the Hop On Hop Off bus. As a bonus, your accommodation will likely be in a beautiful old building. In Moscow, stay anywhere close to a metro station. Moscow has excellent metro coverage and you may even get to see some of the beautiful Moscow metro stations.
For more tips on travelling Europe, read Top Tips for Babyboomers in Bratislava