If I'm not mistaken, the few scenes in 2001: A Space Odyssey in which the characters are on the moon, but not on the surface, show reduced gravity. Specifically, there is a scene inside a transport vehicle of some kind, in which the characters are griping about the poor quality of the food available to them.
I am less certain about other films, but I do seem to recall a relatively accurate portrayal of Mars' gravity in a movie about astronauts going to Mars to investigate unusual structures, including the famous "face" on Mars. I believe the film is called "Red Planet", but I could be wrong.
The terrible movie Apollo 18 also portrays the appropriate amount of moon gravity, but the only structures that the characters enter are the tiny landing modules (much like the actual modules used by the real life moon landing program), which don't offer enough room to really show the effects of the reduced gravity. The interior is just too cramped for anyone to move around freely, let alone bounce from place to place.
And there are interesting scenes in the aforementioned 2001, in which we can see how the astronauts sent to Jupiter cope with microgravity. This isn't strictly related to your question, of course, but is intriguing enough to bear mentioning. The ship spins like a bullet from a rifle, thereby replacing the force of gravity with the force of centrifugal motion.
However, most movies avoid prolonged scenes portraying reduced gravity, such as the conditions you are asking about, because it is (or at least, until fairly recently, it was) quite expensive to produce such scenes. Floating around in microgravity is actually easier to film (you just need to build a set inside the infamous "Vomit Comet" airplane and keep going up and down until the shoot is finished, which is how most of the scenes in Apollo 13 were filmed) than hopping around in a moderate gravity environment.
The vast majority of space movies tend to avoid the issue of moderate gravity environments altogether. For instance, consider the scene from The Empire Strikes Back where the Millennium Falcon lands inside the giant worm inside the asteroid. The asteroid should have had almost no gravity whatsoever, yet Han, Leia, and Chewbacca walk around in the worm's stomach quite easily, and appear to be subject to the same amount of gravity one would find on Earth.