Space Center Houston (SCH) is the official visitors center for the Johnson Space Center but they are not part of NASA.
They do work very closely with the space agency and display many artifacts from the space program, many of which have been flown in space, but their primary mission is to serve as a museum and an educational platform to teach through the Manned Space Flight Education Foundation.
The facility hosts more than 1 million visitors every year and has an impressive collection of items, interactive displays, and even tours to take visitors over to the Johnson Space Center to see the functioning and historic locations.
Among the items on display you will see the Mercury Faith 7 capsule that Gordon Cooper launched in for the final flight of the Mercury program, the Gemini V spacecraft that Pete Conrad and Gordon Cooper went to space in which at that time beat the Russian duration record for time in space, and the Apollo 17 Command Module that brought home the last astronauts to walk on the moon in 1972.
The largest artifacts on display are the Boeing 747 Shuttle Carrier Aircraft that was used for almost 75% of the shuttle ferry flights from landing's in California back to Kennedy Space Center in Florida. It also carried the Enterprise shuttle, which never flew in space, for all of the landing and approach flights when that vehicle was being tested. Sitting on top of the SCA is the high fidelity shuttle mockup called Independence. This mockup used to be at Kennedy Space Center and was named Explorer back then.
Both of these vehicles now give visitors a glimpse into what it was like inside of them and you can visit the shuttle flight deck, mid-deck, cargo bay, and walk the length of the SCA to learn more about its work and the shuttle program.