My house is a rental, so I renter's insurance. I would check with your insurance carrier and see if you can get renter's insurance on the storage unit without a house as part of the policy. My auto, trailer, and home are all with Allstate, when I added the renter's insurance, it actually decreased the entire premium (multiple discounts apply).
2011 Dodge Ram 2500 Cummins
2012 Starcraft Autumn Ridge 297 BHS