Hi, welcome! If you come to Santa Monica let me know!
LA is really spread out, even compared to other big cities. It is generally not bike-safe because most neighborhoods don't have a lot of bikes so people aren't looking for them while driving (Santa Monica and Venice Beach being two exceptions that are safe and have bike rentals. May be others I don't know about). You could definitely bike to the LA Zoo and Griffith Observatory and the Hollywood Sign (all which you should see). You can take the train (Green Line) to Chinatown and downtown. Hollywood itself you could theoretically bike to in the same time public transit takes (1 hour), but I'd recommend an Uber for practical reasons. Santa Monica Pier and Venice Beach would take 1-2 hours by car or by train. You can take bikes on the train and it would be much cheaper, so that's an advantage.
Food is fairly expensive in the tourist areas, get it in Glendale and take it with you.
Public transportation is cheap but buses are always stuck in traffic and the trains don't go directly to a lot of tourist areas. I highly recommend seeing the surrounding hills and the trails, especially in the Santa Monica mountains. that area is my favorite place to go on weekends.