When I was an undergrad at Case, I used to store stuff every summer at the U-Store-It on Warrensville Center Road (near I-480) in North Randall. North Randall itself isn't exactly the nicest place in Cleveland, but the facility itself is super nice. It's completely gated, and then you have to have another key to get into the building where your unit actually is. The whole place is climate controlled and extremely clean, and they sell these locks (they're like 20 bucks, but I highly recommend them) that are keyed and cannot be cut through unless you've got some heavy duty equipment. Oh, yeah, and there's a security alarm and cameras and stuff. All in all, I'd highly recommend it.