Well, I used to live in the Wilshire District and worked in downtown. In my spare time I rode all over Hollywood, West Hollywood, Griffith Park... I never rode on the sidewalks so I can't tell you how cops will react. Just like guitar playing, it takes a little while to develop a callous to make riding comfortable. Watch for the potholes. I had one on Santa Monica Blvd take out two rims at once, and I had just put them on at the beginning of the trip. Ouch.
Check out these sites
CICLE
Bicycle LA.org/
best-bike-commuter-in-los-angeles-county/
L.A Bicycle Coalition