Just out of curiosity, what size city do you live in?
I'd love to have a self-driving car so I could spend more time at my mother's instead of leaving early so I don't fall asleep on the 2 hours of boring interstate to drive home. And that's just one example. It's a 5 hour drive to Chicago; I'd love to just pull on the interstate and let the car take over for the ride home after a tiring day.
In town for groceries and shopping is probably the last place I would let the car take over. There are more variables, but speeds are slower, and it would keep me in practice. Long drives on the interstate, where there are fewer variables would be the first place I'd use it. Sure, the speeds are faster and accidents are worse, but the cars around you are all going in one direction, approximately the same speed, and there are almost no stops, so less to react to. And if the cars can talk to one another it would be even better.
Add in infrared detectors to spot the deer in the ditches in the middle of the night and I'd be set.