As i am visiting Moscow, i went to see the Museum of the Cosmonauts. Basically the space and space history museum.
The russian name of the museum is Музей Космонавтики and is located in the monument to the conquerors of space (Монумент Покорителям космоса)
The monument is an incredible structure made of titanium and representing a space rocket taking off to the space. It is at the end of the cosmonauts alley and it is really worth to see, even if you dont visit the museum.
Easiest way to go there is to take the orange metro line to station ВДНХ.
The museum itself is really interesting. It explains all the different missions launched by Soviet Union as well as by Russian Federation. A room is dediacted to the designers and researchers of rockets and first spaceships as far as 1880.
A nicely documented part is explaining the launch of the first object in space (спутник) and the history of Yuri Gagarine, the first human in space.
A huge part is also dedicated to more modern spacedhips, satellites and corresponding missions.
If you are visiting Moscow, i really recommend you to visit it.
I spent more than 3 hours in the museum. You may plan less time if you don't read russian since the majority of the information are in russian language only.