How about a fire pit? if you get a movable one you cOuld take it to your next place potentially.. then again I've found they only last like a year unless you protect them from the elements.
Arrange your chairs around the fire pit.
Some potted plants would look nice.. altho they would be a pain to take with you so maybe not?
Maybe some artificial ivy for some privacy? I havnt tried this personally but it would be cheaper than a wood fence while still being attractive.
Could get some cute looking solar lights to light up the space? Altho that's usually string based(is there anywhere to hand them?) or stabbed into the dirt(lack of dirt).. altho some of the ground type look like pucks without the stake part.