One of 14 visitors centers that NASA maintains, this one is located at Johnson Space Center, home of Mission Control. Fascinating for all ages, the exhibits range from command modules used on actual space missions to the speculative gadgetry of science fiction. Visitors can at times watch astronauts train for missions. And you can also actually touch a piece of the moon.
If you go:
Open daily all year long except Christmas, with slightly longer hours in the summer. Pick up a Passport to Explore, and you can get discounts to apply to food, tours, and admission to other NASA visitors centers.
Links:

1601 NASA Parkway
Houston, Texas 77058 USA
Phone Numbers:
Space Center Houston
+1 (281) 244-2100
+1 (281) 244-2100