Austerby,
Welcome to the US! I am a California native and been to those places many times. I've been to Yosemite 16 times (my count may be off slightly). All the suggestions so far have been good. Bring water everywhere, especially Death Valley. Make sure you have your reservations ASAP.
You will want to get sunrise and sunset shots in Death Valley. Color film is very good there. The warm tones of the Panamints in the warm sunrise begs for color.
In Sequoia, make sure you hit the big trees. That is a must do! Your number two spot should be Morro rock (the Sequoia one, not the one south of Monterey). The view of the Western Divide is spectacular. Be careful of the altitude. It is easy to faint or get dizzy if you push yourself too hard. Number three, if you have the time is to take the walk to Half Moon Meadow. It was John Muir's favorite spot. Bring bug spray. If you have time visit the underground caverns.
In Yosemite, stop at Inspiration Point on the way in. You have probably seen 100 pictures from there. Go for walks in the valley. It is awe inspiring to be standing next to the one mile tall vertical cliffs that form the valley walls. The valley floor is one mile high. Take it easy at first. Go to Glacier point. Walk to Vernal falls. Go to Yosemite falls. The water should be good in June. If the Ansel Adams gallery is open, spend a little time there. On your last day, so as to adjust to the altitude, drive to Toulemne meadows and Lake Tenaya. DRIVE don't walk there. Bring plenty of water. It's almost at two miles of elevation (9,000ft?) See how many places seem familiar from AA's images.
I see Carmel and the 17 mile drive as a one day event.
Las Vegas is OK. Check out the lights and night on the "strip" and on the downtown outdoor overhead display at night. The view and tour of Hoover Dam is good use of time.
The big sequoia trees of Sequoia and Yosemite are old and large beyond description and unique to that one plot of land. The extreme vertical, glacial carved scenery of Yosemite is very special. I have not found a place in the States like it. The scenery of Death Valley is grand. Carmel is a nice ocean shore place. Las Vegas has shows and nice outdoor lights. Hoover Dam is impressive.
For camera stuff. Bring two bodies. You'll be in places where there are no camera shops. Bring the very wide lenses. You will need them in Yosemite. You will need the normal complement of moderate wides, normal, and short teles. A fast lens would be good for night and in the Sequoia caverns and Las Vegas. Bring an auto-up for shots in Toulomne. As for film selection, the time spent in the trees will be in open shade with no sun. You will need a slight faster than normal film if you like to keep fast shutter seeds and narrow apertures. Use color film for some early and late shots in Death Valley. If you take pictures in the Sequoia caverns, it is low level tungsten light. For filters in addition to the normal B&W colors, bring an "extreme" UV filter for Toulemne, Morro rock, Glacier point, and Inspration point. It will eliminate the high altitude haze that will show up on your film, but you can't see with your eyes. A polarizer also helps at altitude, but is tought to use with an RF.
Sounds wonderful. I'll be passing through Carmel and Monterey in early June. I am picking up my son from the University of California at Santa Cruz. Maybe we can wave as we pass each other on the road in Carmel or Monterey!