Most of the “rescues” as opposed to shelters require that you have a home visit, an application, and usually an interview. The reason they aren’t really “same day” adoptions is because they go through a process to make sure the home is a right fit for the animal, and the animal is the right fit for the home to avoid any of the adopted dogs/cats from being returned/surrendered. I think its worth going through a reputable rescue if you don’t go through the humane society because you know the pets have had their proper vaccinations and medically are cleared. Lucky Dog Animal Rescue and Homeward Trails have many pets on their website and I’ve had great experiences with both. You could probably check craigslist for people trying to surrender their pets, but for many reasons I wouldn’t recommend that.