Getting around a new city is honestly half the experience of traveling somewhere, because you see things you wouldn't see if you just took the standard routes that everyone else takes. When you've got your own wheels you can turn down random streets and discover places, plus you're not stuck waiting for the next train or trying to figure out which line goes where. Look at the rental car options in Moscow at
https://getrentacar.com/en-US/russia/moscow . You'll find plenty of cars available from locals, and having your own ride gives you tons of flexibility to explore the city and get out to those historical spots outside Moscow whenever you want. Just pick something comfortable for driving around and you're set for exploring your heritage properly.