>I only have 2 hives that are registered in my town.
That you know of. I bet there are many more feral ones around.
>How many flights will a queen make to find drones to mate with
Anywhere from one to several.
> and how does she find them?
I don't think anyone knows for sure, but the drones have "flyways" that tend to follow tree rows or roads to a Drone Congregation Area (DCA). The queen seems to follow these, but flying lower and flying further. The drones usually fly about 1/2 mile to a DCA. The queen usually flies 1 1/2 miles to a DCA. In this way inbreeding is usually avoided. My guess is the queen catches a wiff of the pheromones on the flyway and follows them to the DCA. The drones catch HER pheromones and chase her. If you take a helium ballon on a string and put a caged queen on it and "troll" for drones you can sometimes find a DCA and you'll see a "comet" of drones following the queen.