I am a regular contributor to the Thorn Tree Message Board
, operated by the Lonely Planet guidebook publishers. If you go to the US section, you will find all sorts of threads that cover a lot of what interests you. You will also find a lot of discussion about the merits of transit vs. renting a car.
A couple of practicalities. If you plan to enter under the Visa Waiver Program, don't forget to register with the ESTA web site at https://esta.cbp.dhs.gov/esta/
. ESTA is a pre-clearance that verifies that you are eligible for the VWP and that yo aren't on some list of undesirables. Your airline won't let you board the plane without it.
If any driver is under age 25, rental car companies will usually tack on a daily underage surcharge of US$15-25. You can often get a better deal on a rental car by booking through a UK web site.
It will probably be impossible to get lodging in Yosemite in June at this late date, unless you join a tour. It books up very fast.
You've been getting a lot of advice about how hot it will be. The California Coast, north of about San Luis Obispo will be cool and foggy. You will want a sweater or light jacket for that and for San Francisco.
Besides the Madonna Inn, San Luis Obispo has a terrific Thursday Night Market--part farmers market, part music fest, part craft fair, part food festival. They close down the main street for it.
The drive up highway 1 in California is one of the most iconic. It can only be done by car; there is no transit. Hearst Castle
on highway 1, was built by a newspaper publisher with grandiose ideas and too much money. It's not a castle in the European sense, but a rather amazing house complex. You can only see it by tour, and you should book ahead as tours fill up.
Just north of Hearst Castle, you can stop & look at a colony of elephant seals
. In June it will mainly be young males, not a huge as the 2000 kilo adult males, but worth watching. And it's free--you just pull into a parking lot.