Have you thought about just getting a locked box at any of the normal everyday storage places. You should be able to find one for cheaper than the "Automotive" specialist places. Why pay extra for a place that will charge you to or included adding gas, charge your battery and limit the hours you can get your car? Any normal storage place will have a guard and 24 hours cameras and anytime access.
When I bought my NSX in the Bay Area and shipped it to Houston, I used a place called Affordable Self Storage near pier 70 on the waterfront. They had lockable storage rooms and open storage parking spots. Granted I only had it there for a few days and put a car cover on it. But it had 24 hour access, a security guard, and was reasonably priced. Plus they had plenty of room for the carrier truck to get in and grab my car. It worked out perfectly. There were lots of other cars being stored there. Granted it was on the water so I wouldn't want to leave anything there for very long outside.
Just wanted to raise the option of not using a specialist place, you would be surprised at the normal places that will store your car trouble free without paying out the nose. Call around and I bet you can find something 5-15 min from your place.
