You can move it to another level, or cut/paste to another level. It can't be changed in Properties window.

I'm pretty sure the bottom limit is the Associated Level of the view you placed it in and you can not change it.

I've only had success with cut and paste.

Or you can Delete it and then Place it again.
When you Delete a Room, you've probably wondered about that warning about the Room remaining in the project.
This situation is exactly the reason for that.
You don't want to completely toss everything about that Room. It's probably got a Room Name, Department and Finishes, and maybe even an Occupant.
If the Room was permanently deleted from the project, you'd lose all that.
Instead, Revit keeps that information and makes the Room "Unplaced"

What you can do is Delete the Room from the incorrect Level.
Then switch to the Level you want to Room to reside on.
Click the Room tool and notice on the Options Bar where it normally says Room: New, you can now drop down a list.
The Room you just deleted will be in that list (sorted by Room Number, so make sure you know what the Number was)
Pick your Room from that List and place it where you want it and voila! All the parameters are still there.