Sounds like the perfect time of year to visit Death Valley National Park in California! By the time you're there, snow skiing will probably have started in the Sierra mountains. Lake Tahoe probably has the largest number of ski areas to chose from. Joshua Tree National Park in southern California is popular for desert scenery and superb rock climbing. If you don't mind big cities San Diego and Los Angeles usually have nice weather and great cycling opportunities year 'round. The "Big Sur" area of the California coast, between Monterey and San Luis Obispo, is justifiably famous, though the weather may be dreary. If you're in the area, the Monterey Bay Aquarium is worth a visit. Hearst Castle, in San Simeon is also worth a visit if you're traveling along the coast. Don't bother staying in San Simeon, though; Cambria or San Luis Obispo are much better options.
Depending on when you arrive, parks and destinations in the Sierra mountains may or may not be easily accessible. Yosemite National Park draws a lot of people in with spectacular scenery. It can be even more dramatic in winter, but also more difficult to access. I'm also a fan of Lassen Volcanic National Park, which is further north. I thought the cinder cone in the northeast corner of the park, near Butte Lake, was incredibly cool but it's only accessible via dirt road... which might not be passable in the winter. Further north, Redwood National Park and the Avenue of the Giants are great places to see redwood trees; expect lots of rain, though. Those aren't the only places, however. Muir Woods National Monument, for example, is easily accessible from San Francisco.