I've been involved with a couple rescues. Basset and All Breeds.
None of them did same day adoptions. However, if they had already done the house checks and filled paper work etc then they would do dog hand offs.
The SPCA only goes to one pet store. once every two weeks. It keeps things simple and people know where to find them.
When we first started with them they used to have a vested dog with the adopt me sign that would walk the front of the street with a handler. That is how we found them. Since they don't do it anymore, people don't really know they are there IMHO. Their website tells the schedule too.
Basset Rescue used to rarely do store front days. But always did everything back in the day through flyers etc. Now they use their web site to let people know what thy are doing. Most of the time of is community events where they get the name out.
Right or wrong, the one way that organization names stick out in my mind is when they are at the Super Pet Expo. For years now I still remember the rescue groups that are there on any given year. While they don't do rescues, they are there for info, sell a few trinkets and have the cutest dogs out to collect money and get the rescue name out there.
The group we got one of our dogs through seems to be everywhere and yet no where. They divide their time between 3 areas of the state. It seems difficult for them to fid a central location as their location is statewide.