Starting from Carson, go west across Torrance till you get to the ocean. There is a bike route that goes all the way from Rancho Palos Verdes to Malibu. You can get to Santa Monica and then go inland to see Beverly Hills and Hollywood (though this may be longer than 2.5 hr round trip).
If you want climbing, there are some good hills in Rancho Palos Verdes, and lots of climbing inland from Malibu, though that is likewise going to be more than 2.5 hr.
You can also go east to LA River and then take the bike path that runs along the east side of the river to Long Beach and then take PCH (Pacific Coast Highway) south as far as you want.
What you _don't_ want to do is go north or northeast (going directly from Carson to Hollywood might look like a good idea, but it really isn't.)