Drapery might indeed help the ambiance, but you are essentially a tenant (albeit under unique conditions) and may well be limited in what you can do to your temporary home. Drapery usually requires drilling holes for the rod and I highly doubt you would be allowed to do that. You could possibly use a tension rod fit inside the recess but I don't think that is what you are going for.
I have had good luck with 3M Command Strips (as did our daughter in university dorm) but I'm not sure they have anything that would accommodate a rod.