Culver City is a good starting point for a lot of rides. You can take the Ballona Creek bike path to the beach. From the beach, you can head south into the South Bay - Manhattan Beach, Hermosa Beach, Redondo Beach and up into the hills in Palos Verdes. You can head north through Venice and Santa Monica and up into the hills above Santa Monica or north on PCH into Malibu. Map My Ride has a lot of good stuff on there for these areas.
I know that sporteve, a women's sporting goods store in Culver City, is having Sunday morning group rides: http://www.sporteve.com/workshops_events.html
You might also check the LA Tri Club - some of their group rides are open to non-members.
I'm not sure about rentals, but the folks at Helen's Cycles (Marina Del Rey, Santa Monica, Manhattan Beach and other places) might be able to help you find something. Other LBSs are Performance, Bike Attack and Cynergy, all in Santa Monica. Wheel World is in Culver City - I've only really been there once but they might help too.