I remember when I restarted my file that I had to retry at least 10 times before I found a map layout that I liked. My guess is that the amount of maps are infinite, but I don't know for sure.
I believe that there are a set number of them, but it is also a high number. I know someone made a chart of all of the different layouts, so I'll see if I can find it for you!
EDIT: Here it is!
http://bidoofcrossing.tumblr.com/post/39914277511/the-above-video-shows-you-how-the-map-choosing
Beat me to it! 117 maps there.
Technically, there is infinite amount because if you factor in the grass types, that means 468 different types of maps.
then rocks
and native fruit
and station/town hall looks
and maybe placement of permanent locations such as re-tail
still technically not infinite, but for all intents and purposes its infinite