Not too surprising you guessed it was Ballard.
Depending on where you live and where you're going, crossing the locks is a great way to bike downtown. Also sometimes the Fremont bridge route is going to be shorter. I hate riding my bike over the Ballard bridge, but I'm not sure I'd call riding on it "risking death".
Bike access within Ballard is pretty great since the hills are a bit more manageable than in other parts of the city.
All that aside, it's pretty easy to live in Seattle and not have a car, being able to walk to groceries, bars, restaurants, parks, etc.