Near Line 1's Muxidi station ( ●
map ). The entrance is not clearly visible (can see the exit doors)-to enter you have to take some stairs down (may be a bit hard to find). Once you enter, you tell the staff at the desk your ID number to get your free pre-booked tickets (book online or call them). I spent about 3.5 hours here and saw most of everything. It's not the most amazing museum, but it's alright if you have nothing else to do and a couple of hours to kill. Oh and there are some vending machines for you to buy some snacks/drinks
The 5th floor is divided into sections of old Beijing life, like marriage customs, spring festival, and hutong, etc.-It has some displays/models and a couple of decent videos (in Chinese).
The 2nd floor is like a historical timeline-the inner one with displays of Chinese artifacts, maps, and pictures, and the outer one (on the wall) has photos and maps (in Chinese) of seemingly random pictures/photos of people/events/places deemed important for the period. Each picture has a one liner description in English and a few more lines in Chinese. The selection seemed a bit random and the descriptions are not that great, but it's still interesting to see (especially the maps [labelled only in Chinese] showing various powers/civilizations throughout time.
Other floors displayed chinaware and Buddha statues, as well as some temporary exhibits.