Assuming "hard" self-driving...
Education: more kids "driving" themselves to school. There's an age where a kid could be trusted to walk alone, but not ready to "drive" there. Get in car, car takes kid to school & back. The one thing stopping my kids from going to a preferred school is we can't drive 'em there at that time; give me a trustworthy car and I'll let it take them there.
Play: like above, parents will be more likely to let the kid travel a non-trivial, non-walkable distance to play with friends. No longer bound by parental availability, parents can just authorize the kid to get in and be taken somewhere.
Parking: there will be a "Napster"-type stage of anarchy where self-driving cars won't park, they'll just slowly roam around until the owner calls it back. I've spent a whole day in NYC driving in circles (while the family enjoyed scenic stops) in lieu of finding & paying for expensive parking; would be nice to just get out and let the car wander, using roads as "parking in motion". This will lead to legislation & new solutions requiring aimless vehicles to actually get off the roads, albeit into more compact storage.
Tourism: lots of people dislike dealing with taxis. I'd certainly be more comfortable with an automated "pick your destination on a map" UI, evolution of getting rid of elevator operators.
Travel: huge hit on travel industry. My family rarely flies anywhere, opting instead for painful overnight 1000+ mile drives. Many people will be far more likely to do such trips when they can get on a major long-haul freeway and completely ignore the driving process. No more trying to stay awake on a boring overnight drive, just doze off completely, waking up only for refueling or nearing destination. I'll happily drive the complex parts at start/end, but it's that 700 mile stretch that's agonizing as driver.
Housing: longer commutes will be more tolerable. I will live in an acre+ site, and let the car deal with traffic while reading/working/napping. So long as I can ignore the commute, I'll put up with a much longer one.