I didn't do much traveling while I was in Russia. When we first arrived, our visas were contingent on staying in Moscow proper until we could get them extended. By the time we were applying for extensions to be able to leave the country, we were sent home due to the pandemic.
The trip to Moscow is quite exhausting, over 24 hours between flying and layovers.
I used the Metro quite a bit if we went to the city center. If we're just going to the grocery store or out to dinner, most things were within walking distance.
My favorite activity we did early on was going to the Lenin National Library. They have millions of books there; I think the only place with more physical books is the U.S. Library of Congress. The Library is absolutely beautiful with a grand staircase at the entrance and reading rooms throughout the building. These reading rooms are important because you cannot take books out of the library. You print a request through the library's computer system, take the receipt to a librarian who then sends it up a pressured mail tube to the librarians who work on the stacks.