I think parking will be less of an issue. Think Uber/Lift with autonomous cars. This would be especially true in cities where parking costs can get ridiculous. The fleet would spread themselves out based on historical data and probabilities on where people are likely to request them from. I could see systems that will automatically call a car while you are waiting at the registers of stores so that by the time you are a the front door, a car is reserved and waiting there.
I think the biggest hinderance to fully autonomous cars will be the illogical nature of the human psyche. At some point, these cars will be advanced enough that they will be significantly safer than human-driven ones and will start making life-and-death decisions based on the rules that will reduce overal loss of life and limb to the human population in general. For example, image that the car as been put in a position where it needs to decide whether it is likely going to kill two people or kill one. Which path should it choose? Most people would say kill the one instead of the two. Now, what if the car is yours and you are the one person?
Even though the chance of a car getting put in that position might be orders of magitude lower with autonomous cars over manual cars, a lot of people will not like the idea of their property chosing to kill them to save two complete strangers.