It's recommended to rent a car or use ride-sharing services for transportation. There are also biking and hiking options for some of the parks. Expect travel times to be around 30-40 minutes between locations.
If you have less than 7 days, consider visiting only 3-4 locations for a more leisurely trip. However, if you have more time, there are many other nature destinations nearby such as Joshua Tree National Park, Channel Islands National Park, and Griffith Park.
Los Angeles International Airport (LAX) is the closest major airport to Calabasas, approximately 23 miles away.