I went through this last year and wound up storing at my Mom's apartment parking garage. He was covered but it had open sides. It was cheap and worked but while researching I found a place in Leesburg that was more affordable than any of the other options and your baby is well cared for
http://www.leesburgcarstorage.com/
he had a 6 month minimum but if you're really polite and nice and explain the situation he'll probably waive that. He told me he would have waived it.
The car is indoors and on a trickle the whole time
The other options I found were all just too expensive. The storage units that can hold a car run around $300 a month.
This year we have a garage but it's a single car garage. So my plan is to buy an outdoor blow up pod and put Tigger in that. From what I've read they work really well and they can handle rain, snow and ice hitting it. We used to live in a townhouse so that wasn't an option there.
Good luck, I understand the search. Hope this helps