"The good news is that autonomous cars don't need to park-- they just go give someone else a ride. They could change city life forever."
This will not change with autonomous cars. If people didn't want to own cars, the above situation could exist _now_ -- they are or were called taxis/taxi cabs/cabs/hansom cabs/licensed hackney carriages.
Yes and no. In principle people could do that and certain very high density areas, they already do. However, outside these areas, relying on taxis is too expensive and inconvenient. Further, the cost of car ownership is lower since parking one is neither difficult nor expensive.
Autonomous vehicles will greatly reduce the cost of taxis. The cost reduction means there will be more of them so they will be more convenient too. I expect many more people will choose to go car-less in that environment.
I don't expect all them will give up their cars, though. I'm not even sure that most of them will.
Self-driving cars do actually have to park.
Private self-driving cars will need to go somewhere to wait. It won't need to be all that close but they will need to go there. This may actually increase traffic on freeways and arterials as self driving cars head home after dropping off their owners, only to return again sometime later to pick them up. One round trip turns into two.
Self driving taxi will not be able to stay usefully in service all the time. They will need to park somewhere or circle uselessly, which is arguably worse.