three cities in one week, i really don't think its possible. I lived in california for 4 years (now i am in madison,wi) . I did a road trip to  SF to LA, LA to Vegas and back to Sf with two of my friends in 5 days , but belive me we didn't do a lot cause we didn't have that enough time to do everything. So , I would say you should give atleast 3 days for every cities, still it will be a hectic scheldue of must do things in all these cities. Before you start your trip, plan what do you want to do in each cities.
I don't know how you plan to travel, air or car. If you have money in the bank , i will suggest travel by plane , you will have plenty of time to enjoy.