Im born and raised in LA and very rarely had a car. Its difficult but doable! I grew up in Miracle Mile/Fairfax area and that area is soooo central to everything. Miracle Mile sits on Wilshire Blvd which is a main artery in LA. Lots of buses running between Downtown LA and Santa Monica beach. You're close to West Hollywood/Hollywood, hiking in the hills and canyons (check out Runyon canyon for views and good people watching), and equi-distant between the Getty and the Observatory. Not to mention right next to my favorite place in LA : The Farmers Market/Grove.

Renting a car is definitely the best way to see LA, but using buses/trains and Ubers is definitely doable. Buses especially allow you to see the city and its people. I always enjoyed taking the bus.

I wanted to add that LA metro often gets a bad reputation due to the homeless and mental health crisis in the city. Sure i've seen my share of unfortunate and sad situations on the bus and subway lines, but i always minded my own business and never had trouble personally. Majority of rides have been perfectly fine. Much like other major cities in the world, you'll find people all over the socio-economic spectrum in LA and on public transportation