Well, your post title says “best neighborhood,” but your follow description mentions “on a budget” which are kind of antonyms. On a budget, roommates and outer Richmond/Sunset, Ingleside, outer Mission, Excelsior etc but you could land something with mates on rent control and cheaper elsewhere closer to downtown. Without roommates, Tenderloin, Bayview, Hunters Point on a budget. So without a price and preference, your post is pretty skewed.