Richmond district is pretty far out there and generally gets the worst of SF weather. It has two things going for it: Amazing asian food on Clement street and some classic SF house/hill spots...oh shit...3 things...fort miley is in the outer richmond. You'll enjoy it despite it being kind of an out-there district.
You might want to try airbnb. People in SF tend to be pretty tech savy, while constantly looking for ways to pay rent, so I bet you could find some reasonable stuff right around the richmond area- its full of residential areas.
Best way to get around is to mostly use your skateboard and ocassionally hop on a muni train or bart to get to far-off areas. Honestly though, I've skated clear across the city from the presidio to the border of bayview and potrero hill a few times without really having a problem. Unless you are in a rush to get somewhere at some point, just cruise around, bomb a couple hills, walk up a few, and you'll probably see all sorts of spots from videos that you recognize.