Our dolly is primarily stored behind and under the RV when parked unless the site is long enough to just keep it hitched up. When we had the RV in storage, it went behind and under the rear of the RV as well.
If you must use a dolly, be sure and put a hitch on the rear of the TOAD so you can tow or move the dolly. Some campgrounds will require you move the dolly (and possibly the TOAD) to a secondary parking space, or you may not have room otherwise. The hitch is just good insurance to allow you to move the dolly easily.
I never had a problem at a campground storing the dolly. At home, I certainly have no problem. I currently have four trailers and a 1985 Suburban stored in the pasture. Oh, yeah, I forgot the 48 foot antenna tower that is laying out there, waiting to be completed and put up.
But, I sold my dolly. I really wish I had not done that!
Charles- you bring up a good point as to home or campground. I was thinking of covering the tow dolly with a tarp or building a lean to that would be attached to my storage shed. For the campground I would do as the situation allowed, as many campgrounds are setup with many different camp sites.
At home the dolly is parked behind the motorhome. I try to get a pull through site whenever possible If the site is long enough, then I leave the dolly connected to the motorhome. If not then I pull in, then back the car off and put the dolly anywhere out of the way. Some times once the car is off, you can leave the dolly connected and fit in the site. With a back in site, I back the car off the dolly and move both car and dolly out of the way and them back in to the site.