Let's see which ones I remember off the top of my head. All directions are based on how the map first loads, i.e. the river is in the south and the mansions in the hills are in the north.
Lizards and birds spawn at the criminal hideout, with a snake spawner right behind it at the mine entrance. There's also a bird spawner on the Parrot family lot, and I often see a bird north of the saloon/east of the cat jungle. The dirt path south of the Hydrangea House and Honey Darnell's home frequently has a pet nearby somewhere, too; I usually see a bird or turtle there. The City Hall has a lizard spawner in the back. Check near the Equestrian Training Grounds, too, I often see a lizard behind the barn and a snake behind the training area (both spawns are outside the lot). Another lizard spawner is immediately to the left of the beach lot. The Cinnamon Crest fishing spot has a bird and a turtle spawner, the Water Treatment fishing lot has a turtle spawner and there is usually a bird or two in the hills behind the lot as well. The cat jungle has a rodent spawner, which I find rather amusing.
Other spots worth checking are the fenced-in field east of the two empty 30x40 lots near the beach, the small field between the Miller and Riffin homes, the small "corral" off the dirt road leading to the Fox ranch and the fenced-in area with the hay shack north of the cat jungle/east of the consignment store.
There are likely more, but those are the ones I remember and check most frequently.
