I think maybe in 1-2 cities in limited areas I will be able to use an app on my phone to order a Google car from point A to B. I think it will have lots of limits, perhaps limited to certain areas within a city, perhaps limited by speeds, time of day etc.
I don't think it will be long distance, most cities won't have it, highways later, etc.
So, in other words, no. Not to pick on you but the scenario you (optimistically IMO) describe is that, on a test basis, under certain limited circumstances and locations, might be able to have fully autonomous vehicles. (Though if they're that limited, why would they be legally allowed on the streets?)
And highways actually seem like a more likely nearish-term scenario given that, aside from the occasional deer/moose, debris, and construction (which could presumably be dealt with in various ways) seems far more manageable than the typical city street.