@LMK5 in most cases, cost is the driving factor for off-campus Housing. In some cases, lack of continuing student availability is the driver, and in some cases the need for more room is a driving factor.
Leases in the immediate area almost always goes from June-May. I think people start looking around Feb-March but it depends how picky one is. Often I see last minute offers on Craigslist or Facebook or Reddit even as late as Aug 1 (though I definitely wouldn’t wait that long).
Applications for on-campus housing start on Feb 1 and offers go out in mid-March.