Moscow's Second Kremlin
On the outskirts of the city in the northeast corner lies a second Kremlin made entirely out of wood. And while this may sound interesting in and of itself, it happens to be home to the largest outdoor open market in Moscow (probably all Russia as well), where you can buy literally almost anything from Russian dolls and hats, to old Soviet memorabilia, to chess sets and jewelry, to honey and vodka, to Beatles albums (which my dad bought) and pretty much anything else one of the vendors found in their basement. Occasionally, and I kid you not, I have even seen refurbished uniforms from the Second World War, so the sky's the limit on what you can expect to find.
The market is fairly limited on the weekdays but on Saturday and Sunday it stretches on for hours, so you can pretty easily lose yourself wandering (as I have done multiple times) gazing at the extensive variety of people's accumulated stuff. Most of the vendors know very little English aside from numbers, so a knowledge of some Russian can be enormously helpful especially when haggling, which brings me to my favorite aspect of the market. Everything can be haggled down. Literally everything, and it is expected that you do. And most of the vendors are willing to get into long discussions on price, so if you have the patience, or are just looking for another odd way to practice Russian (the main reason I often went here), you'll walk away spending far less than you would at any gift shop within the city.