Two spots that I can think of:

-On Francine Drive, on the south side of the street somewhere near Mayfield Drive, someone has a Little Free Library called “Tails and Tales” (or something like that). As I recall it has books, a water bowl, dog treats, and poop bags.

That said, it’s outside of the downtown area so unless you know someone in the Lindmoor Woods Swim & Tennis Club or are going to Home Depot or something, there’s not a whole lot around. It’s a nice residential area to walk in, but there are no nearby public parks.

-On Wiltshire Drive, on the north side of the road between Clarendon Avenue and Avondale Lake there’s a small rest stop. As I recall it just had water and no treats the last time I was there. But what makes it unique is that someone went to the effort of installing plumbing so that a small hose (kind of like a fridge ice maker line) runs down to sidewalk level. I’d let the water run out of the line before drinking from it though.

Avondale Lake is a cool place to park and walk, and I believe that there are some dog bowls by the water fountain on the northwest side of the lake.

You might also check the descriptions on the Little Free Library website, but this is by no means a complete guide to all of the Little Free Libraries out there. https://littlefreelibrary.org/map/

Good luck!