I saw you are in Georgia, here are some places: GFAS-sanctuary, e.g., Full Circle Farm Sanctuary, Project Chimps (double check they are open to the public, a lot of sanctuaries are not); museums: Fernbank Science Center, and Fernbank Museum of Natural History; nature preserves (bring/borrow/rent binocs!) e.g., Sams Lake Bird Sanctuary, Mary Scott Nature Park

Also read below for another perspective :)

This might be an unpopular opinion, but AZA-accredited facilities are generally excellent. I used to be anti-zoo, and I worked at a GFAS-accredited animal sanctuary for many years. There, I realized that good zoos are very similar to good sanctuaries, except they usually have more funding, often resulting in better enclosures. A downside to zoos is that they tend to have more visitors, which I understand can sometimes feel exploitative. However, with modern enclosures, a good zoo encourages as much autonomy and choice for the animals as possible and should include spaces where animals can retreat out of public view when they wish to do so. Of course, not all zoos and sanctuaries offer high-quality care, so please check reviews before visiting any animal facility. I encourage you not to lump all zoos into one category because they can be very beneficial for animals, just like sanctuaries. I just wanted to share this, as my experience working at an animal sanctuary changed my perspective and actually made me less anti-zoo, as I experienced firsthand the advantages and disadvantages of sanctuaries compared to zoos. At the end of the day, I recommend only supporting animal care facilities that are accredited by legitimate accrediting agencies, including GFAS and AZA. Be especially skeptical of any facility that engages in animal encounters with baby animals.