What month? What budget? March and April are a lot different than June and July in both places.
The safest route from Monterey IMHO is back to San Jose then through Manteca and route 120 to Yosemite.
You should price check the San Jose airport vs. SFO.
Another option, to get to Yosemite is take the San Joaquin train south to Fresno and rent a car at the airport.
By all means, see the aquarium while you are in Monterey.

Last week of April. It something is worth it, we will spend it. What is IMHO? Thanks for the info...

IMHO - In My Humble Opinion

Definitely look at flying into SJ rather than SF if you aren't planning to visit SF itself. SJ is an hour closer to Monterey/Carmel.

Lodging for Yosemite will probably be the limiting factor in your plan, so if you don't already have reservation somewhere, I would see what I could get and then build the rest of the itinerary around that. April isn't high season in Yosemite, but lodging is limited, so it is pretty much always full.

Because time is short, I'd try for something IN Yosemite Valley itself - Lodge at the Falls, the Ahwanee if your budget stretches that far. I don't care for Curry Village much, but it does have the benefit of being in the valley and if nothing else is available, it might be worth it. Outside of the park is the town of El Portal which has some places. The Tenaya Lodge outside of the south entrance is very nice - but it is a drive into the valley, so that's a trade off.

For the coastal portion of the trip, I would definitely put Santa Cruz on your itinerary - either as an overnight or as a day trip from Monterey (45 minute drive). Santa Cruz is a fun place and I think a must with teenagers.

Monterey and Carmel have a lot to offer - Carmel is more romantic and upscale whereas Monterey is more lively. They are within minutes of one another, so you can see both regardless of where you decide to stay.

Point Lobos, south of Carmel, is a must-see for gorgeous coastline, easy hikes, and animal-spotting (sea otters, harbor seals, tide pooling, birds, deer, rabbits, etc.).

The Big Sur coastline is absolutely wonderful, so if you have time, you could drive south on hwy 1 a ways and check that out.

Of course the aquarium has been mentioned. If the weather is good, you might want to do some kayaking on the bay or take a boat trip.

From Monterey it would be MILES out of your way to travel back up to San Jose and across to Manteca to get to Yosemite. Not only is it farther -- it would have you driving through the seriously congested South Bay, Fremont, Pleasanton, Tracy etc etc.

And Amtrak makes no sense whatsoever.

As november_moon says -- the main issue is where/when you can get accommodations in Yosemite Valley (or possibly Yosemite West which has the closest non-park accommodations).

So book your room(s) at Yosemite Lodge or wherever first. Then build the rest of the trip around that.

I agree with others that staying in Yosemite is the best idea, if it is available. If not, there are some type of cabins at Curry Village. I have never stayed in them, but maybe someone has and can share info. However, the Yosemite View Lodge in El Portal is only a couple of miles from the Yosemite entrance station (but further into the valley). It is affordable and decent, and although nothing spectacular, sure can be a lifesaver! They also have a restaurant (not many in this area). Sequoia NP is just south of Yosemite and also a fabulous place with huge redwood trees.

For the route between Monterey and Yosemite, I wouldn't go through SJ either. In fact, when I drive to Yosemite from SJ (where I live), I head south and pick up Hwy 152 at Gilroy and then go east. I would go with one of the following:

* In good weather - this route takes you in the south entrance of the park, and while it takes longer, your first view of Yosemite Valley will be at Tunnel View, which is spectacular:

Hwys 1/156/152/99/41.

There is actually a small shortcut at the town of Madera that connects 99 and 41, so there is no need to go all the way down to Fresno - you'll see the road on the map.

* If the weather isn't good, I'd come into Yosemite through the Arch Rock (west) entrance on Hwy 140. This route has lower elevations the whole way - no passes to cross or anything - so in the event of snow at the higher elevations, this is the route you want:

Hwys 1/156/152/59/140

I actually don't care for the Hwy 120 route - it is steeper and has more shear drop-offs. Plus it is the furthest north, and since Monterey is to the south, it is out of the way for you.

Thanks for all the info! We have a room booked at The Ahwanee for 2 nights. We will certainly fly into SJ instead of San Fran. We would like to spend a day at Kings/Sequoia. I think we will do that the night before we go into Yosemite. All of the information is great, as I have never been to that part of CA before. There is so much to see, filtering it out can be hard. Keep the suggestions coming!