I went to the cosmonaut museum a few years ago. It was nice, though fairly small. 1 hour should be enough to see it, unless they're adding a lot. It's under the base of the giant rocket sculpture.

VDNKh also has a Vostok 1 on display outside the old Cosmos pavilion. There are some space-related exhibits in the State Central Museum of Contemporary History too.

Lenin's tomb is open 10-1 Sun, Tues, Thurs, Sat, but has frequent closures beyond this, particularly if there's an event in Red Square. No bags or cameras are permitted, and respectful decorum enforced. Lines can be very long for just a minute or so walking through the building, and if you're still waiting in line at 1 you're out of luck.

Touring the Kremlin itself is a must-see.

Note that non-Russian entrance fees are much higher than for citizens, and are strictly enforced. A docent at the Kremlin made my Russian friend show ID after she overheard him talking in English to me.