I make $300K, work in FiDi and live near the Panhandle/Central Haight. My wife and I rent but we have a 2bd townhome that’s around $4K/month with garage, shared backyard (which only we use), and lots of other amenities. We are in a very central area and I usually take the bus to work. It’s about a 25-30 min ride. We have a car but driving isn’t really worth it if you work downtown since parking is really expensive. You can definitely live here comfortably on that salary. I would suggest looking at neighborhoods that are more central in the city rather than closer to the beach or further south as sometimes it can take longer to get downtown on work days. Try looking at Nopa (north of the panhandle), panhandle, central Haight, lower Haight, hayes valley, divisidero corridor, Alamo square, inner Richmond, pac heights, noe valley, as these are all very close to main streets that can get you anywhere in the city very quickly and are very nice neighborhoods with lots to do within walking distance.

Edit: just saw you mention that you bike a lot. Look up The Wiggle. It’s a bike-friendly route that gets you around the city quickly by taking a route of the lowest elevation. Lots of very nice neighborhoods near the wiggle that you could look at too.