I would see if this kind of lock would fit and use it. I'd like to see someone cleanly cut that. I may actually switch my lock to this. http://www.amazon.com/Master-Lock-40DPF-Shielded-Stainless/dp/B00004SQKX/ref=sr_1_8?s=hardware&ie=UTF8&qid=1454177043&sr=1-8&keywords=padlock
I've always had good luck with this Public Storage in NRH:
I've used it a couple times between moves, etc. They are climate controlled, seem reasonably safe, and are pretty cheap compared to most places around. Guess it really depends on how close it is to you though.
My big tip for storage units if you haven't used the before, they all have break ins. Get 2 of these disc locks:
https://smile.amazon.com/Master-Lock-Padlock-Stainless-40DPF/dp/B00004SQKX/
and put them on the door. Any lock pretty much can be cut/broken into, but those are harder than the typical "padlock" style and its one of those things where if a thief sees one unit with two of those vs a unit with 1 padlock, they're more likely to cut the one padlock, take the stuff and run, then spend the time to mess with 2 disc locks.
You can get some good (for practise) Masterlocks on Amazon for pretty cheap. Apparently the safety locks are really good for practise as they have some security pins in them.
http://www.amazon.com/Master-Lock-40DPF-Shielded-Stainless/dp/B00004SQKX