I keep all my extra plastic and little terracotta pots in my tiny greenhouse that I used a few years back. Basically, it's just a shelving unit with a plastic cover that I started using for the pot storage. I put the cover on it so that rain water wouldn't accumulate in pots. Thing One and Thing Two however thought it had a much more useful purpose...shredding the plastic so they could then rip apart and disperse the plastic pots all over the yard.
All the pots are now in a large plastic tub that is secured tightly on the porch. I'm thinking that I've pretty much puppy proofed the backyard unless they decide they need to rip out the few things that I do have in the ground. Fortunately, they've not showed any interest in these and they've had ample opportunity.