You're in the high dollar area, Alpharetta, and they probably don't appreciate trashy trailers. I used to work at the Phillips Electronics office there off of Windward Parkway.
You might check with Camping World in Woodstock on Hwy 92@I-575 or move on up to around Cumming to see what is available up there. A little further away in Marietta is Three Way Campers, nice people, and I think they have RV storage there but that isn't too close to where you are. I live on the west side (Douglasville/Hiram) and $30-$50 is the norm around here. You are getting advice for everyplace except Atlanta Georgia area. Beside this post I only saw one other post relating to our area.
I did a Google search for Cumming and Classic Self Storage on GA400 had outside storage over 24' for $60/mo. Sawnee Storage was $65 for 40', North Lanier was $45-$65 for uncovered, double+ that for covered. Most covered is around $150>. I don't know if that helps but I guess you just have to shop around but get a little further out from the hustle and bustle.
There is a camper sales place in Buford, a little further out.
2014 Palomino Puma 25RS
2011 F-150 Super Crew XLT
Days camped in 2014 - 23
Camped 2015 - 47
Camped 2016 - 51 done - 6 more planned so far