"You would have to do some real homework to find a campground with nearby shopping."
Not really.... Catalina SP is a huge beautiful CG that has hook ups and some of the best hiking in the area as it sits at the foot of Mt Lemon. My only objection to Catalina SP is that they do not allow wood fires of any kind. Directly across the street from the entrance is large shopping center; Walmart, theaters, Best Buy, Dicks, restaurants(Olive Garden, The Keg - great steakhouse, even an In and Out). Just down the road is Home Depot, Chile's Target, Fry's... just about any store you would ever need is within a mile or two.
I would not recommend trying to drive a quad on the streets of Tucson, as noted it is a large busy city but from Catalina SP you can easily walk or bike to the shopping center. Downtown Tucson is about 12 miles to the south and there is limited public transportation available.
:C