LA-Area Cyclist Dopers: Route Advice Please!

I will be in LA, specifically Venice, for the next several months for work. I am looking for some advice about various weekend bike routes and getting around. I have a Specialized hybrid, so I am fine with paved roads and reasonably well-maintained gravel-type paths. I also have a car with a bike rack, so I am not particularly concerned about getting around to starting points for fun weekend rides.

I am looking for any and all suggestions on fun rides in the range of 5-50 miles. During the week I’ll be commuting around 8 miles from the coast to UCLA and then back each day, so I suppose rides on the shorter side might be preferable on the weekend!

I do have a few questions:

  1. Is going to Catalina Island worth it for biking? I don’t want to pay for the permit to ride in the interior of the island and I doubt my bike could handle the interior. Is there enough in Avalon to be worth my time?

  2. I am planning to make an afternoon Kings game. Is riding Venice Blvd from the coast straight to the Staples Center reasonable? There are bike racks at the Staples Center.

  3. I gather that it is truly impossible to ride a bike to Dodger Stadium. Is my best bet riding to the metro station at Western/Wilshire and taking the metro/trolley to the stadium?