We're from DC and spent 11 days in CA in February and split the time between Lake Tahoe, Yosemite, and San Francisco. Obviously much different than the summer, but we skiied in Tahoe, hiked a bit in Yosemite, did all the touristy stuff in San Francisco and the area just north.
Based on that, I wouldn't recommend Yosemite on its own, simply cause I think 7-10 days would be a bit much. We only had 2 days there, which wasn't enough time, but we also had feet of snow to contend with, along with a 2yo who complained of walking everytime we started hiking (though the kid never stops moving normally so we thought we'd be okay). The bus tours were cancelled due to snow while we were there so we couldn't even do that. We did some basic hikes, but didn't see much of what we would have liked to since some paths were covered in feet of snow, some roads were completely closed, etc. Had we gone in the summer, with longer daylight hours, I would think 3 days would be sufficient. Also, if you stay in the park (we stayed at the Ahwahnee), there's sort of just 1 restaurant, which would get annoying after a few days I am sure.
San Francisco we had 4 days and got to see all the major stuff, including the zoo, which eats up time, and Muir Woods. I would skip the San Fran aquarium if you are going to Monterey as theirs is much better. We would have liked to spend more time just walking around in various neighborhoods, but again, February, so it was 40 degrees and raining the whole time, so with kids, not so much an option. We stayed at an incredible place, the Fairmont Heritage Place, Ghirardelli Square, which is sort of a hotel/ownership composed of condo units that are really incredible. The price was actually really good and we were upgraded from a studio to a 2 bedroom, which was incredible. And having 3 Ghirardelli stores/ice cream shops right outside the room was of course a great bonus.
But I'm digressing.
Anyway, I posted because I thought you could incorporate a few of the places you mentioned. If you did San Fran/Monterey, you could also add in Yosemite. The drive isn't terrible and none of those places really need more than about 4 days a piece, at a max. If you did 3 days at each and then allowed a half-day to drive between San Fran/Yosemite (and a little less for the Monterey part), you'd be fine.
ETA: Just read the above post and I agree! We are also pretty commando, but we do still have 2 small kids, so not as commando as you could be. We wrote out our itinerary in advance, booked the hotels based on that, and stuck to the plan. Not much room for error when you have the rooms booked and stuff (and in Yosemite you need the 1 restaurant booked in advance too).
And if you don't want to be all commando like that, then I would do SoCal. Less driving and stuff, so it would be a little more low key.
