The Best Friends Animal Society would be good. They have domesticated animals and some wild ones. I have a blog post about it if you want some photos and details. 

The nearby scenery is pretty awesome, too.

Volunteers are needed during the loggerhead turtle nesting season—from late November to March every year at Mon Repos Walking Track
near Bundaberg in Queensland, Australia. The link below has contact info to find out more.

https://www.ehp.qld.gov.au/wildlife/threatened-species-week/south-east-queensland.html#loggerhead_turtle

I have never done this but my cousin volunteered at The Rhino Orphanage rhino orphanage in South Africa and has some amazing pictures/experiences.

I would recommend the ARCAS Wildlife Rescue Center in Peten in Peten, Guatemala.

It's been a few years since I was there but I loved it: their wildlife protection program is very good and their remote location is beautiful.

Check out their website for more information: http://www.arcasguatemala.com/

Guatemala is also a great country so if you would like to combine volunteer work with some traveling that would work very well in Guatemala.

My two recommends are the David Sheldrick Wildlife Trust - Elephant Orphanage near Karen in Nairobi as well as the Marakele Predator Park in Thabazimbi, South Africa.  Both great organizations doing excellent work.

There is a very nice place In Puerto Limon ! Costa Ricacalled Sloth Sanctuary. I would say this is THE perfect place to volunteer with animals. Check it out on internet!

saludos!

Check out Earthwatch.

I worked on a hippo sanctuary in Ghana on the Black Volta river a few years back.

They have lots of what the call "Expeditions" and not just with animals.

I went to Costa Rica with a group who did Sea Turtle conservation projects. That's a big one in CR. 

In the Santuario de lapas NATUWA, Costa Rica.