Originally Posted by Tycho Brahe

I doubt you will spend all your waking hours on a bike. The bigger question is what else would you want to do?

Without a car, you will be miserable in some/most of the locations suggested. No clue how old you are, but I would stay in Studio City or Hollywood (both are very close to Burbank) and just enjoy Griffith Park or Mulholland Drive (both in the Santa Monica mountains). You can then walk to get food/coffee/whatever.

I only do climbs, so that is all I can suggest. Ascents up and down to Mulholland are fun! Parts of Griffith Park and the nearby river path are flattish.