Anza Borrego would be the most convenient to San Diego. I tend to hit Joshua Tree and some of the other areas in the Mojave desert so haven't driven in to Anza Borrego from these routes - although family members use portions (from Julian on) for spring flower trips, etc. From Laguna, I'd suggest south along the coast and then go inland on the 78, through Escondido, past the San Diego Wild Animal Park, through Ramona and Julian and down the Banner Grade. Family members use the 76 and 79 but they are coming from other areas and those would be less convenient.
These aren't really fast roads east of Escondido, so you would be spending some time on the driving but the area should be pretty pleasant and greened up during the time you are talking about.
Since I don't frequent Anza Borrego, I'll leave it to others or the sources offered as to whether you would want to return via Julian or go south to I-8 and then west to San Diego.
But Joshua Tree and especially Death Valley would be completely out of the way.
I would certainly start trying to make reservations now if you want to overnight as there aren't a lot of options if not considering camping.
