My 11-year-old daughter wants to volunteer at an animal shelter - to help walk and groom the dogs & cats, etc. I would accompany her. I would like this to be a positive experience for her, so I am looking for an upbeat, well-organized, not depressing place.
I recommend one of the no-kill rescue groups or shelters. You could start with Animal Humane. If they don't have a location near you they will likely be able to give you a zillion rescue group names.
For example, we got one of our rescue dogs from PACA which you can find via Google. They place dogs in foster homes and bring them out for adoption drives. Though it's better than alternatives, our dog was stressed out being in a pack in someone's home. That foster mom would have happily accepted a little help. Her heart was in the right place.
I've seen lists with more than 20 local rescue groups -- some that focus on a specific breed and others that collect adoptable animals at the kill-shelters. I think the mag "High Desert Dog" publishes some group names but I can't recall for sure.
You can also ask at a locally owned pet store (not a mega store). I go to Long Leash on Life and they would definitely help. If it were me, I'd have an easier time if I wasn't driving across town and there are so many groups in need of a helping hand.
The city shelters do euthanize and my very limited experiences there were very depressing. But maybe the animals there are most in need, I don't know. Any rescued dog or cat will thrive on a little extra love and your daughter may even help to make an animal more adoptable.
I applaud you for supporting your daughter! Good luck!