Mount Barker has one I think it's called Adelaide Hills Storage and there is an area down Lonsdale way.

What do mean by south of Adelaide - there's caravan storage on Daws Rd and many caravan parks offer storage facilities.

the cheapest we found was in gawler. Its a guy who owns a couple paddocks. Wierd guy tho. likes to meet prospective storers to see if they get on. If you do google search you will find him.