I'd skip the entire trip for Yosemite. My very favorite place in CA. Might be hard to get reservations this late in the game. I think it is better to go there earlier in June to see the waterfalls really going good. Of course, each year is different, with enough snow it might still be going good in July.

Six of one, half a dozen of the other, really hard to say.

If you could fly in and out of Oakland (rent and return your car there also) then a quickie trip to Yosemite might be doable, but only if you travel very early in the day to avoid the traffic jam from the Bay Area to Yosemite. Also, as spirobulldog has mentioned, lodging into Yosemite might be hard to get even now. It has to be overnight, because after the long drive, you still have to enjoy Yosemite without the urge to have to get out after just a few hours there.

If you arrive midday in the Bay Area, you could drive immediately to Yosemite, lodge overnight somewhere outside the park, see the park all the next day, then return to the same outside hotel for the second night and get a really early start the following day for the Bay Area.

There's a lot to see and do in Yosemite and you'll be shortchanging yourselves if you do a quick in-and-out.

I'd suggest that you look carefully into what there is to do in Yosemite, decide what your priorities are there, and then decide whether you want to include it in your trip or not.

Otherwise, take spirobulldog's suggestion and just stay along the coast.

This is the official site for booking lodging inside the Park.
http://www.yosemitepark.com/lodging.aspx

Because lodging can be booked up to a year ahea, it may show as full. However, there are always cancellations along the way, so you need to keep looking almost on a daily basis to find lodging.

It's up to you.

South of Carmel is Point Lobos state park which has magnificent trails. I think we did two or three of them and they were each wonderful. Lots of birds and the view of the coast was breathtaking. It is a lot closer drive than Yosemite would be.

I highly recommend Yosemite but not as a half day trip after driving there and out again on the same day. You want to give Yosemite ample time.

Can you cut out some time in the city proper to make at least an overnight at Yosemite?

How about something like this:

Day 1: Arrival in SF
Days 2 and 3: In SF
Day 3: Early am drive to Yosemite - overnight in Yosemite
Day 4: Morning in Yosemite - afternoon drive to Monterey
Days 5 and 6: In Monterey area
Day 7: Drive back to SFO for flight home

This allows you to see all 3 areas in 1 week and with an overnight in Yosemite.

I would probably skip Muir Woods and spend days 2 and 3 in SF proper - you don't want to shortchange the city and you will have lots of nature during the rest of the trip.

For your time in the Monterey area, with 2 days you can take a drive into Big Sur, explore Monterey/Carmel, and maybe even have time to go up to Santa Cruz to go to the Boardwalk and the beach there.

You could easily spend your entire week in any one of those places. I'd choose two and divide your time between the two. It would be easier to add the area south of SF rather than going to Yosemite.

If you do go to Yosemite, I'd give it at least three days so you also have time to visit the high country. The valley will be very, very crowded that time of year and, as spirobulldog posted, the waterfalls won't have much water that time of year.

I wouldn't short change Monterey area or Yosemite. Just do one. I like Yosemite best, but coast is really nice too.

If you really want to do it all, go with November Moon's plan. Especially if you don't plan on getting out here again soon. If you want to take it slow, then you will need to choose. Like picking a favorite child.

Monterey has a fantastic aquarium that your kids should like. And don't forget to research Point Lobos. The website is attached below. It was fantastic and not far from Carmel at all.

http://www.parks.ca.gov/?page_id=91

In July all you will pack in at Yosemite is finding parking places driving endlessly to do do. Skip it.

The high country of Yosemite wont be crowded. The valley will be ridiculously crowded. But the high country is lovely.

I like November_Moon's itinerary. We did the Yosemite/Monterey part when our kids were just slightly younger than yours and we cancelled our 2nd night in Monterey in July. Just too cold.

Thank you for all the thoughts! Lots to think about. Unfortunately, we only have a week to spend in the area. I'm leaning Yosemite for a time we could spend more time there but need to discuss with my husband. He's thinking the opposite.

If we did Yosemite, we were thinking of almost exactly what November Moon laid out. Arrive in SF midday Saturday so we'd hit Yosemite midweek. But as JCarlinsv and others have said, crowds will be an issue.

Suzie, I loved my summer in Monterey because it was cold! I hate the heat and humidity of summer in the mid-atlantic.

Oh, and I looked at lodging availability and it seems our choices are a $325 room at Tenaya Lodge or a canvas tent at Curry Village for half that (and hope HPS isn't an issue).

Keep checking since there are frequent cancellations in Yosemite. People make their reservations a year in advance and plans change.

Also you can get closer to the valley than Tenaya Lodge by staying in El Portal at Yosemite View or look into Yosemite West lodging which is in the park but not through the park's concessionaire.