It wouldn't be a successful trip to Moscow without a Moscow Mule. Luckily you don't have to stick to tourist bars to do so. Delicatessen is a basement bar and down a strange side street that you would never expect to walk down. It appears as though you are walking into a back parking lot but as soon as you turn left down a small alley you can see the Delicatessen wrapped outside entrance. It is super cozy and very chill. They are best known for their vodka drinks (of course) but have a large well stocked bar. The decor is a bit mixed but with the feeling of hanging at grandmas.
You certainly won't find any tourists but you may find some expats.