The reservations for June 15th to July 15th open up Feb 15th and they go by a lottery system. These reservations go within a few minutes. Search here for Yosemite lottery to get hints on how to win one.
Yosemite ReservationsWe've made the trip several times once in four and a half days, heh, from North Florida. You don't want to do that obviously. We didn't either but we had Valley reservations and they are not easy to get. There are commercial parks west of Yosemite but we have never stayed at one always managing to get into the park. It's a long drive into the Valley from those places.
The usual way is I10 west , diverting around New Orleans on I12 back to I10 and then west to Arizona then I17 up to I40 that west to US395 north and that into the west entrance to Yosemite via Tioga Pass. If Tioga pass is open then. We just grin and bear it to get thru Louisiana.
You will pass near Death Valley and that may be worth a division for a day or so but it will be HOT. We do manage to drive to points of interest and get out of the vehicle for 30 minutes or so without problems. Joshua Tree will also be toasty but not as bad as DVNP, you should be able to a campsite inside that park but do not delay making reservations. They have had various problems in that park so check to make sure it will be open when you get there. It's been many years since I stayed there.
I haven't stayed in Sequoia or Kings Canyon.
As for Cali, fuel will be very pricey as will groceries. The roads in general are horrible, worse than anything Louisiana has to offer. I just stay out of the state as much as possible which is one reason we prefer the 395 route. It is in a part of the state that is the least problematic. Taking the west side roads up to Sequoia and Yosemite will lead you into the heart of the Cali road system and I would add a day or so to what you would usually expect it to take. You can get into the west side of Sequoia from 395 but only into the western edge of the park. You know that there are plenty of Sequoia Trees inside Yosemite don't you?
Assuming you visit Yosemite last I suggest taking US 50, aka the countries 'loneliest highway' across to Utah. That will run you right by Great Basin NP which is worth a couple of days. 50 is worth the drive by itself. Just fuel up whenever you can and keep the tank above 1/2.
Have a good trip Yosemite is absolutely amazing, nothing else is like it in the world.
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