The last place I had one was the convenience store on the south end of downtown Gilbert, but that's pushing two decades ago at this point. The main place I think of for Slush Puppies is in convenience stores. Each of the major c-store chains has frozen drinks (7-Eleven's Slurpee, QT's Freezoni, and the widespread Icee are some examples), but these are different from Slush Puppies because the Slurpee et al. are made with a carbonated base, while Slush Puppies are non-carbonated. Since the big chains are out, I think your best bet for finding a Slush Puppie is going to be checking mom-n-pop convenience stores.
A close competing product is Dairy Queen's Arctic Rush (formerly the Misty Slush, formerly the Mr. Misty), which the last I knew was made in a fashion very similar to the Slush Puppie, unflavored sweetened base with flavor syrup added to it.
My husband was crazy about them as a kid, but I could never find them anywhere! Finally one day I was driving down the road, saw a Slush Puppie van and FOLLOWED IT!!! He told me how to find them, and at the time I found a store at Thunderbird and 32nd Street or Cave Creek. I can't remember now. Even with online resources it is really hard to locate them!