The spin you're referring to is the first single spin that car thief Jackson (played by Michael D. Roberts) does as he's in control of KITT at the intersection of Wiley Canyon Road and Tournament Road certainly looks like where that happened :

but I'm referring to the second spin, when KITT has taken over the driving and KITT fries the tyres doing several donuts ... there is a large shopping centre / mall in the background, so it's somewhere else :

I tried to read the signs on the buildings in the background :
- (Conrad?) Ice Cream (on the corner)
- some sort of clothing store
- (Homber, Holbes ?) market
Do the logos / fonts / colours of those shops look familiar to anyone ?
I couldn't find your reference to Old Road in Canyon County ... is that the exact name of the road ?
I will keep looking on my end too ...