Go to the splash park at the Pier, perfect to get the sand and salt off after beach, before you get back in the car.

https://www.sanddollarfl.com/activities/splash-park-st-johns-county-beach-pier

If your family doesn’t mind spooky things, take a spooky walking tour through the downtown St. Augustine.

your list looks good! It is such a fun, historical city and I definitely recommend the ghost tour! I grew up in the area and visited often. Ripley's museum was also a cool little adventure!

Ripley's is fun. Definitely the Alligator Farm. You can go on day/afternoon cruises from the marina downtown - they used to have a pirate ship one. (link but check Groupon for deals: https://www.blackravenadventures.com/) I LOVE the fort. It's a huge grassy area that's perfect for picnicking and you can often spot dolphins that have come into the bay. Even with younger kids, you'll want to make sure you have some time to walk down St George St and the side streets. The old city gates mark one end and there's a super cool, old cemetery right there, too. A couple of blocks away there's a great park your kids would probably enjoy.

My #1 recommendation is to be careful of timing. Summer can be absolutely miserable with heat and humidity. If you aren't used to it, it's not enjoyable. Also, if you can get a sitter or adult time, I would suggest a tour of San Sebastian Winery. I grew up near there and went to college in St Augustine; it's one of my favorite places!