Hollywood studio tours

Can't answer on the tour question. As for lodging it depends a lot on budget. My first choice, having grown up on the West side of Los Angeles, would be somewhere in Santa Monica. It could be quite warm in July, and closer to the ocean is cooler for sure. Plenty of food choices around, I would not focus too much on a hotel breakfast, they are usually overpriced, and not a good representation of food quality for the area in general.

Check out the Getty Center if great art is an interest, it's free other than the parking, and is spectacular. There is a ton to see and do, of course, that is not Hollywood centric.

When I was a kid I was friends with one of the sons of a celeb, and had a tour of Paramount Studios around 1970-71. I suspect they don't do them like that anymore.

I live in L.A. and know quite a few people in "the business" here. One works as a head animator at Disney and it's extremely difficult for him to being people in for a visit, even in his position. They are extremely sensitive about anyone possibly seeing anything that would let the cat out of the bag or be stolen by innocent looking corporate spies. I believe the last time they allowed organized tours was back in 2015 - even with those tours they only shuffled you into a theater, showed you the history of Disney, and then had you exit through a gift shop.
One of the only ways to get in is to go as part of an animation convention. I put a link to the big one that happens in November and, although I know that's not when you'll be here, I included the link because it has a great list of all the animation studios in L.A. Who knows!!?? Maybe give them a call and see if they'd be willing?? All they can say is no!
http://www.ctnanimationexpo.com/axStudioTours.php
A great place to stay is the Beverly Garland Hotel in North Hollywood. It's over the hill from the main part of Hollywood, about a mile from Universal Studios. It's out of the way but within easy reach of everything. If you want to drive by Disney Animation Studios they are just a few minutes east of there along the 134 freeway - you can't miss it on the north side of the freeway! Giant Sorcerer's Apprentice hat as the entrance. Although you can't go in, it's still fun to see!

May I suggest the La Brea Tar Pits and Museum for the 9 year old and the "kid" in all of us?

https://tarpits.org/

It's a small but very nice museum. Educational in a fun way. Shouldn't take more than 2 hours to visit.

Here's some suggestions where both you and the kids would be happy:
If you like hot dogs, Pink's is famous. IMO they have the best chili dogs. Be prepared to wait 30-45 mins in line, but worth it.
Any In and Out Burger is good.
Tommy's Burger is good too, but I like their tamales with chili best.
Food stalls at the Farmer's Market. http://www.farmersmarketla.com/
My favorite are the caramel covered marshmallows. Du-par's is famous for their pancakes.

Since you mentioned touristy things and specifically the Chinese Theater, Walk of Fame (Stars), etc., be aware that that part of town can be a little seedy, granted, there are many fun and interesting things to see. You're not going to get mugged or robbed, but there might be things you don't want your 9-year old to see. I agree on the Getty Center. Fantastic art exhibits, fantastic architecture of the premises and great views overlooking L.A.

From what I can find, doesn't look like any studio does the private tour anymore. Would have been cool to see how/what my son will be doing for the rest of his life!

Thanks everyone for the suggestions of other things to see and do.