I would agree that Florida (I did this last year on Tampa side) does benefit from the car due to lack of public transport, but you may find that Uber/Lyft makes your reach slightly greater (heading down to Lake Tohopekaliga). As everyone seems to mention, have a look at ebird, which will allow you to see the hotspots around the area and then use google maps to check how far it is by road. A rough calculation for Uber would be 1.5 x miles (not exactly)
For a future possibility, San Francisco and the bay area lends itself well for different birding destinations by public transport. The local Audubon Society (GGAS) also has lots of monthly bird trips (including midweek ones), so you can meet with others in the morning, and then carry on or move on if you wish. 3 weeks travel for about 220 USD (70 Bart/Bus, 130 Uber and 20 Airport Shuttle). Some people I met did give me lifts back though (or to nearest BART).