I wouldn’t have space in my apartment for the life-sized version of the Time Machine, but I’d be more than happy to own the working model that propelled Rod Taylor’s cigar into the future!
You can have the Natorum Demonto, 
The letters of transit are an inspired choice. Somebody already claimed the rarer avis, and a medical tricorder that didn’t work would just be too painful, so I going to choose one of the submarine sandwich style guns from Galaxy Quest.
Now I want the 18" high Stonehenge. That would be awesome.
It’s too late to change my request?
Beat me to it. Second choice is Priscilla from the movie of the same name. Bit hard to store though.
Can I have the firehouse from Ghostbusters?
I was going to say the Ferrari from Ferris Bueller’s Day Off, but it’s just a replica.
It’s still worth it, though.
Ferris Bueller's Day Off Ferrari sells for $337K with no engine .
There are of course countless replicas for purchase. Somehow, the Coen brothers or their wardrobe designer seem to have forgotten to protect the design.
No movie sets, just props.
I’d love to have Camelot from … Holy Grail, but it’s only a model.
Yes, I know where the door is.
Is that so you can see how heavy (or not) it really is?
Partly!
It can’t be real gold.
Just an iconic bit of Godfather memorabilia I’ve always admired.
I saw the piano at the Academy Museum in Los Angeles.
I tend to think of sets as fake rooms built on a soundstage. The Ghostbusters firehouse did (and I think still does) exist as a real building.
As for other props, the oscillation overthruster would be kinda cool, even if only a few people would recognize it.
Oh, that reminds me. How about a flux capacitor?
How about the African Queen, or the steamship from Fitzcarraldo? Tough to display in a trophy room…
You’ve got a place to store them, of course? 
Jayne’s Hat or The Marquis de Carabas’ Coat
An episode of Lost in Space (TOS) had the Robot being the leader of an army of little Robots. I want a little Robot.