Something to think about: Will your son be getting a Hogwarts Letter and supply list? You can find templates online to make one yourself, or there are several Etsy shops that do an amazing job with personalized letters, metallic inks, and real wax seals. Some even send the letters out with stuffed owls.
Also, don't forget you can go to the bank and exchange your muggle money for Gringotts bills that you can really use to make purchases in Universal like buying your school supplies, a pet, robes, or lunch. This doesn't involve riding the ride, so you can still do that later to preserve the timeline.
If you are trying to follow Harry's footsteps exactly, I'd do:
1. Breakfast at the Leaky Caukdron first.
In the books Harry came here first as you had to go through here first to get to Diagonally.
2. Money exchange at Gringotts.
You can tell them you want to setup an account and exchange money. The goblins are interactive and will talk with you. You can buy a vault key pin here as well. You can get them other places, but it's more fun to get your key here.
3. Madam Malkins for robes
Harry went here next.
Make sure to check out how you look in your new robes in the mirror
4. Next Harry visits both the Apothecary and Flourish and Blotts for school supplies, and Hagrid gets his owl from Eyelops Emporium. You can pose for pics outside these spots, but can't go in. You can buy a pet in the Magical Managerie if you want. You can buy "supplies" in Wiseacres Wizarding Equipment.
5. Olivanders for the wand is last
If you plan on doing spells later, you will need an interactive wand.
Also, since you haven't gone to school yet, you don't know any magic and should wait until after you visit school to start performing magic if you are following the books.
6. Train to Hogsmeade
In the queue, you will get to a spot where the line turns right and then left through brick walls. There is an obvious optical illusion set up here. If you hang back and let your son go ahead of you a bit, you can film him disappearing through the barrier at Platform 9 3/4.
7. Forbidden Journey ride, Hogwarts Castle
I recommend doing the castle only tour first, so you can stop and listen to each character speak and get the full storyline. This also gives you time to take pictures and take in all the little details. Then go back and ride.
8. Flight of the Hippogriff
This would be next as Harry visits Hagrids house in book 1 and flies on the Hippogriff in book 3
9. Honeydukes Candy shop and the 3 Broomsticks Resturant
Harry sneaks into both of these in book 3, he could visit here anywhere from book 3 through 6
10. The Twiwizard Spirit Ralley show
This would be next, happening in book 4 as well as the Dragon Challenge ride also book 4
11. Hogshead Pub
Book 5, the kids hold a DA meeting here
You can order Butterbeer here
12. Send a letter or postcard home or to a friend by owl mail
You can bring your own, or buy something here.
Don't forget the stamp.
13. Take the train back to Diagon Alley
14. Quality Qudditch Supplies and Florean Fortescue's Ice Cream Parlor
These are places Harry visits in book 3 and could visit anytime after
15. Weasleys Wizard Wheezes
The twins opened this shop in book 6
16. Knockturn Alley
Harry follows Draco here in book 6
17. Tales of Beedle the Bard
These stories are mentioned in book 7
17. Escape From Gringotts
This is last happening in the middle of book 7
A few other thoughts:
I'd do spells as I go, or if you have more than one day, I'd return first thing in the morning, during early entry if possible, and do the spells when everyone else is riding FJ and Gringotts. There usually isn't a line in the morning for spells, so you can take your time, do them more than once, get good pics, and not have the outcome spoiled by the person in line in front of you.
The Knight Bus is introduced in book 2, but doesn't really fit in without lots of backtracking. Technically, as an underage wizard without access to transportation, it would be believable for you to take the Knightbus to get to Diagon Alley.
The phone booth
Harry visits the Ministry in book 5
It would take backtracking to fit this in in chronological order
Celestia Warbeck Concert
Harry never attends one
You can here Moaning Myrtle in the girls bathroom in Hogsmeade, not sure about the Men's restroom
Take time to explore. At many of the fake shop fronts, you can hear what's going on inside the business if you walk up to the doors and stop to listen. Exploring Windows is also worth the time.
You'll need to put your purchases (except things you may be wearing like a robe) in a locker before riding, or you can send them to the front of the park or back to a resort room. This can make doing all your shopping first, like in the books, a little tricky so keep that in mind.
Hope you have a great trip.