Slang (usage generally the South, ex. Alabama) for a convenience store attached to a gas station, such as a 7-Eleven. The word 'zippy-doo' intends to encompass the idea of a trip to one of these stores being 'speedy', essentially. As in "I need to fill up my car and am kinda hungry, so I'm just gonna stop in the attached zippy-doo," 'speedy'.
Other spellings: zippeedoo, zippy doo, zippydoo, zippidoo.
I was craving a soda, so I took a quick trip to the zippy-doo down the street.