The Challenger Center at the University of Tennessee at Chattanooga is one of several centers worldwide offering students simulated space missions (which teach science, math and teamwork in a fun and relevant manner) in honor of the ill-fated Challenger shuttle. But this one has the benefit of being supported by the widow of Challenger astronaut Dick Scobee. A local resident, she has loaned some of her late husband's effects for exhibit.
If you go:
This is an educational facility and not really a tourist attraction, but it is receptive to visitors. And any group of at least 10 may participate in one of the missions by registering in advance.
Links:

855 East 5th Street
Chattanooga, Tennessee 37403 USA
Ellie-Wallis@utc.edu
Mailing address:
Dept. #6406
615 McCallie Avenue
Chattanooga, TN 37403 USA
Phone Numbers:
Challenger Center
+1 (423) 425-4126
+1 (423) 425-4126