Carmel is really high end/ stuffy. Santa Cruz had homeless people everywhere. Monterey is always foggy but more activities. I'd probably pick Monterey.

Carmel is pretty but except for the beach I found it mostly un-family friendly, and I was there several times with young kids. (Fancy date-night restaurants only, little shops selling delicate expensive things, wealthy older people clientele).

If your in Capitola/Santa Cruz eat at Gayle’s, Carpos and Riva Fish House. The Crow’s Nest if you want fancy. On the way from Santa Cruz to Monterey stop in Moss Lansing at Phil’s. As for lodging in Carmel try the Mission Ranch (great brunch as well)...this is Clint Eastwood’s place and it’s not too pricey. The other cheap option is to stay at Asilomar....the old buildings (don’t fall for the new ones)...the lodging is charming but a bit rustic and each building has its own communal room with games/fireplace, etc...so you can put the kids to sleep and have some adult time. There are no TVs.

I like the Dream Inn Hotel in Santa Cruz. It is right on the beach and has a heated pool. You can walk to the Boardwalk.

Agree that Carmel is more oriented toward adults. There is golfing there if you or DH are into this but SC and Monterey are more kid friendly.

And to answer one of your questions directly - no, Carmel is not worth the extra expense for families. It is more of a romantic weekend kind of spot.

Doesn't matter which city, just find the lodging you prefer. This place is on the beach in Santa Cruz: https://www.dreaminnsantacruz.com
This place is in the hills above Santa Cruz: https://www.chaminade.com

And this is one of the nicer hotels in Monterey: https://www.ictheclementmonterey.com

This is an unusual activity that is fun with kids: http://elkhornslough.com

I would stay in SC and travel to Monterey for half a day. They are not that far apart just go early to avoid traffic. When you are in M you could also do whale watching.

Santa Cruz has the boardwalk and Natural Bridges beach. You can rent bikes or e-bikes and bike to Capitola or drive there. Aptos is just past Capitola. This is another cute beach town. If you stay in Santa Cruz I recommend the Dream Inn. Its on the ocean and has a heated pool. You park and then just walk to everything. You could also do airBNB. One caution is that the area off Capitola and Santa Cruz is now a Great White shark rookery. If you are shark phobic anywhere along SC or Monterey may concern you. If the sharks don't bother you, no one has been bit be prepared that water is cold. Make sure to walk down the pier and see all the Sea Lions.

If you travel north up 17 a few minutes from SC there is a touristy place called the mystery spot. It is actually very cool and I normally hate touristy things. You can also see the Redwoods going over toward Felton. There is a train that takes you back and forth to SC which is good for kids. I'm not sure when but occasionally they have Thomas the Train events.

Monterey all the way! We spent two weeks there right after school got out. The weather for us is perfect- cool in the morning, bright and sunny and in the upper 60's in the afternoon. We went kayaking, walked down town, spent the afternoon in Pacific Grove at the Lover's Pointe Beach, hung out in Carmel, spent a day doing Half Moon Bay and all of that. I am jealous! It was a perfect vacation! My favorite place- can't wait until we can retire there! Have fun!

It is much chillier in Monterey and Carmel right now than in Santa Cruz.
I would stay in Monterey (aquarium and beach, weather permitting) and explore Carmel and Santa Cruz. But it doesn’t matter much which town to stay in, wherever the hotel availability is better.

We are heading to SF area shortly and looking to spend a few nights on the coast. Carmel seems to be the priciest but is it worth the higher charge for families? It sounds like Santa Cruz has a boardwalk which my kids would love and then we could do day trips to the other towns?