Randy is a very nice guy and he lives central LA in regard to the highlights of LA.
I've rented Randy's bike (a city cruiser) and had great fun seeing the city.
Try the bikepath from Syd Kronenthal park (near the house) which goes all the way up to the beach. You can choose if you want to go in the direction of Manhattan beach or direction Venice/Santa Monica.
Syd Kronenthal park can also be used as a open air gym. It's walking distance. I enjoyed it very much.
Also try the Metro lines in five directions of LA is recommended.