The Dynamic Test Stand performed a shake, rattle, and roll test on the Saturn V and shuttle to mimic vibration at launch, and the shorter T-Tower ran the spacecraft’s propulsion system through its rigors.
“It’s one of the most recognizable landmarks in Huntsville,” Derek Rose said.
Not any more, but there's always the Davidson Center along 565, address 1 Tranquility Base:
The Davidson Center was designed to house the Saturn V Dynamic Test Vehicle (listed on the National Register of Historic Places) and many other space exploration exhibits. The vehicle is elevated above the floor surface with separated stages and engines exposed, so visitors have the opportunity to walk underneath the rocket.
https://en.wikipedia.org/wiki/U.S._Space_%26_Rocket_Center#Buildings
The Saturn V dynamic test vehicle, designated SA-500D, is a prototype Saturn V rocket used by NASA to test the performance of the rocket when vibrated to simulate the shaking which subsequent rockets would experience during launch. It was the first full-scale Saturn V completed by the Marshall Space Flight Center (MSFC).
Though SA-500D never flew, it was instrumental in the development of the Saturn V rocket which propelled the first men to the Moon as part of the Apollo program. Built under the direction of Dr. Wernher von Braun, it served as the test vehicle for all of the Saturn support facilities at MSFC.[2][3][4]
https://en.wikipedia.org/wiki/Saturn_V_dynamic_test_vehicle
The first stage of this Saturn V is hoisted into position for a shake test at the Saturn V dynamic test stand in 1966.
