Do you have access to a loft (we would call it an attic?) Often you can put something up there that will work just fine. Even an accessible crawlspace would work
It would be better to put it outside, away from the building (and all the noise sources that go along with it), but that's obviously not possible.
Much as I dislike them, active antennas are a decent choice in situations like this one, if you don't have access to a loft. We have an article in our wiki that touches on some of the issues...
Active Antennas KB6RWX - The RadioReference Wiki
Another possibility would be some real thin wire out to a tree - but I am dubious of such an arrangement standing up to a winter storm...Mike