I'm moving to San Francisco from NYC and looking for some helpful advice

Hey all,, I'm a lifetime New Yorker looking for a change of scenery and I have some newbie questions about SF, any advice is much appreciated.

1. What area of San Francisco would be the equivalent of NYC's Williamsburg or the Village?

2. What area is cheap for rent but relatively safe?

3. I hear the public transportation isn't the same as it is in NYC,, will I be able to get around via motorcycle?

4. In general how if SF different from NYC?