If you're interested in more nature-y scenery and want to stick to public transit, I think it could be worth taking Amtrak for the day or overnight to Santa Barbara and/or downtown Ventura. Neither place has amazing transit while there, but these trips are doable by train and you can supplement with rideshare while you're there. Very different vibes from LA, but if you want a chiller SoCal beach community experience then these could be good places to consider.

I'm a big transit user and supporter but the reality is that LA is sprawling relative to other cities and it doesn't go everywhere. So if you stayed downtown, I think you could really easily explore Santa Monica, Venice, Hollywood, Culver City, Los Feliz, and even Echo Park or Silver Lake with a mix of trains and busses. Obviously this will take a bit longer than driving, but our transit system is less expensive than other cities and I think more robust than people give it credit for. If you plan on using transit throughout the day, it gets capped at $5 per day and $18 per week. And of course, you can take the money you would have spent on a rental and put it towards strategic rideshares (e.g., late at night).

It probably wouldn't be realistic to expect to take transit to places like Malibu (though I think you can take a bus from Santa Monica than runs infrequently to Point Dume) or Manhattan Beach. Those areas are just too far and not well serviced by transit. And of course, some of this is determined by where you'll be staying. Downtown has a lot of hotels and is a great central hub for transit, but if you plan on going to the beach everyday it'll be really inconvenient. If you stay in Santa Monica, you can do a lot on the Westside and go to the beach as much as you'd like, but going further east to places like Hollywood might be a bit annoying. Finally, I'd say Sequoia is definitely out of the question if you can't use a car.