I have a couple stands that I want to use outside with potted plants.

The first one is this birdbath:


The second is this stand:


I've gotten pots that fit the shelves.

Birdbath has one 9 inch pot and one 6 inch pot of standard height. Stand has two 8 inch and one 12 inch succulent pots.

I'd ideally like to have vines wrap around the stand and overflow down from it.

For the birdbath, I'd like plants that hang down.

As usual, my requirements are:
Drought tolerant
Sun
Little to no maintenance (no fertilizing, deadheading, etc, but I am willing to prune back occasionally)
Non-toxic to dogs and cats

Any ideas for plants to fit?

Looks like some fun pots! : )

You'll have to research the toxicity on your own, but a few come to mind. If you're sticking with hardy plants, check them for your zone. If you don't know what garden zone you are in (besides "Happy!" LOL!), you can check here:
https://garden.org/nga/zipzone...

Little Pickles (Crassothonna capensis)
Hairy Dewflower (Drosanthemum hispidum)
Graptosedum (XGraptosedum 'Francesco Baldi')
Beauverd's Widow's Thrill (Kalanchoe beauverdii)
Canambaia (Rhipsalis teres)
various Hoyas: https://garden.org/plants/sear...
Striped Inch Plant (Callisia gentlei var. elegans)
Jenny's Stonecrop (Petrosedum rupestre subsp. rupestre 'Blue Spruce')

Here's a list of plants to avoid around dogs on ASPCA site:
https://www.aspca.org/pet-care...
From there, you should be able to find the cat list. Cats are probably going to be less interested in plants that don't move much in the wind, but there's a story somewhere about some cat messing with any plant, at some point.

Thanks. I'm checking those out now.

As to toxicity, I've found that gardenia.net is really a great resource.

Happy to suggest. : ) Best luck!!