One of the most interesting places we visited in MOscow was the New Tretyakov gallery which houses the Soviet Era and socialist realist art; really a must. The older gallery is wonderful but mostly things you can see anywhere in the world; the New Tretyakov has the Soviet art you can only see here (and not even in St. Petersburg where we searched in vane to find Soviet era art).
Just outside the gallery in Muzeon Park is the Garden of Fallen Leaders which is where the unloved statues of unloved despots were dumped and are now displayed:
Unfortunately on the day we were there is began to pour rain when we left the gallery to explore the park and so I don't have as many pictures as I would like, but it was still pretty interesting and I would put it high on the list of sights to see for a visit to Moscow. It is across the highway from Gorky Park and you could combine a visit. We took the metro from the center to the Oktyabrskaya stop and walked to the park.
On the way back to our hotel we took a detour and visited a couple of interesting monasteries -- they are all over Moscow and well worth checking out ones near where you stay.