Reddit mentions of Geology Rocks!: 50 Hands-On Activities to Explore the Earth (Kaleidoscope Kids)

Outside of natural history museums you're mostly going to find paleontologists at work in universities and at fossil sites. There isn't much for someone to do watching a researcher work on a fossil at a university. As someone who does it every day...it's mostly working on computers. Some sites do public digs. However, he's very young to be able to gain access to sites, so it depends on their proximity to areas open to the public.

I don't know the area very well, but there are a few sites that are fairly well known. Have you heard of Sharktooth Hill? They have public digs. I think that would be something he'd have to do in a few years. When I did work at fossil digs that were open to the public there were minimum ages for liability and insurance purposes. It also looks like they allow volunteers in the prep lab, so that's something to keep in mind.

The Page Museum (at La Brea) has a fishbowl lab where people are preparing fossils. Outside in Hancock Park are the tar pits themselves. These are places you're probably familiar with.

You have a few age-appropriate options:

• You mention local museums (and you have a bunch, which is really cool). Have you just been visiting or have you looked into all of the events that go on? You could join a museum you guys love and participate in the special programs. A lot of these museums have great summer programs that go beyond just visiting the exhibits. They often have special events for National Fossil Day and Darwin day that are really fun, or movie nights where they'll discuss the science of the movie. I did events like that alongside curators and other researchers, so they can definitely be opportunities for interactions. He's getting to be the age where these programs are perfect, and I really think they're your best bet. There are often guest talks as well if he can sit through something like that. The Page Museum even says:
  
  > Mark your calendars for October 12 and come to the Page Museum! We will be celebrating fossils found right here at the La Brea Tar Pits as well as specimens collected by NHM scientists across the globe. This is your chance to get up close to real fossils, talk with our scientists, and become amazed by the variety of fossil discoveries to date. The event is Free and open to the public.
  
  
• Get him outside so he can see geology in action, even if they're not fossil digs. This site has recommendations for paleo stuff in Southern California. Anza Borrego looks like a great place to go. Look into some paleontology and geology books for kids (like this, this, and this) and tie them to the what you see outside. This is more about the process of observing and learning about the world. It's about seeking to explain things. He's probably extremely curious and inquisitive and would do well with things like this. Other state parks or public lands in the region may have trails and visitors centers. You're definitely in an area where there are fossils!