When I used to be a student, I passed by these huge buildings daily. During the 1917 revolution they used to store food, in the early 2000s they were another boring state-owned museum. Things have changed since that time. The museum was renovated, the new brand appeared and (what I liked most of all) the Centre for Documentary Films is now situated there too.
As for the exhibitions, I prefer visiting temporary ones. The history of Moscow is definitely exciting and important but there are so many other things to see and do! So the current schedule of exhibitions is always available online. Same with the Documentary Film Centre. Finally Moscow has got a place where you can both watch and discuss new documentaries.
The inner yard of the museum is an attraction by itself. On the picture you can see just 1/3 of the whole area. It’s so quiet and relaxed here, especially after busy Sadovoe ring with 10 lines of traffic. So feel free to grab a coffee in LES coffee-shop (in one of the museum buildings), enjoy the inner yard making plans for your future Moscow discoveries!