It depends, what's your time budget, and would you rather start your trip in So-Cal, or end your trip there? Hotel costs might play a role (like, it will be cheaper at the end of your trip vs. beginning, or vice versa). In general, it's probably going to be more hectic in So-Cal with all of the driving & theme park logistics, I personally would start there.
What airport should I fly into/out of?
Depends where you are coming from, and what your budget. LAX is probably going to be your cheapest option, but most of us hate this airport and its antiquated rental car system and the traffic. Lower volume airports like SNA (closest to Disneyland), BUR (closest to Universal Studios), and LGB (kind of in between) offer a better user experience (like a quick walk to the rental counter), but are often more expensive and/or require a stopover in PHX, LAS, or SMF depending on where in the US you are coming from.
For the north, same thing with SFO (the big airport with better transcon schedules), vs OAK and SJC being the smaller airports.
Getting from North to South, or South to North.
If the bulk of your trip is in So-Cal, it might be better to rent a car for use in So-Cal, return it, then immediately rent another car with the intent of driving it from So-Cal to Nor-Cal (i.e. dropping it off at another location).
Flights are also cheap going between both sides of the state, so consider that. But most people who visit do want to drive US-101 (and maybe CA-1) along the coast as it is one of the most scenic drives in the United States (and lots of little towns to explore/pop into).
If you don't care about view/experience, and don't want to fly, I-5 will get you between north and south the fastest. It's just boring, dusty, crowded with trucks, and smells like cow fart.
Other Misc
Alcatraz is on your list for SF, but consider the Walt Disney Family Museum if you're a Disney fan. It's an extremely dense museum (probably not for little little kids) that covers his life and is, to me, a must visit for any Disneyland historical buff.
Make sure you use the official Alcatraz site for ferry tickets. Some companies sell "Alcatraz" trips that never actually go on the island. That link is this:
https://www.cityexperiences.com/san-francisco/city-cruises/alcatraz/ and it is linked from the National Park Service's website for Alcatraz
https://www.nps.gov/alca/planyourvisit/fees.htm NOTE: BOOK YOUR ALCATRAZ TICKETS THE MOMENT YOU FINALIZE YOUR DATES. Tours sell out frequently, and in advance.
If you have the time in So-Cal, consider an actual studio tour with Warner Bros. or Paramount. The Universal backlot tour is... what it is, but touring the Warners or Paramount lot gets you a lot closer to actual TV/movie production, if that's your thing.
My personal recommendation
If I lived on the east coast and traveling with small children (like, 2 x under 8), this is how I would do it.
Day 1: Fly into LAX direct (no stop overs) and hire a car service and be driven over to Disneyland. Don't go into the parks on day 1, just relax at the hotel.
Day 2: Disneyland
Day 3: Disneyland
Day 4: Disneyland/California Adventure
Day 5: Check out, go to Universal Studios area hotel (hire an Uber or something), half day at Univ. Studios or other activities (like Griffith Park, go catch a show, Museum of Modern Art, California Science Center with kids and see the space shuttle, etc...)
Day 6: Universal Studios full day
Day 7: Check out early and start driving up to San Francisco via US-101. Start the drive no later than 6-7am. Make stops in Solvang, Santa Barbara, San Luis Obispo, etc... Arrive in SF ~6pm (assuming you've made a few hours worth of stops).
Day 8: Alcatraz in the AM (take 8:40am boat), then spend the afternoon roaming (see other sites: Golden Gate Bridge, Ferry Building for food, Pier 39 aka tourist central, maybe catch a baseball game at Oracle Park if in-season, drive up to Sutro Tower if it's not foggy and you want a view)
Day 9: Walt Disney Family Museum -- get there early, because it's a dense museum, you might spend a lot of time there. Afternoon as you please. If not your thing, consider a day trip to Napa for wine tasting, or other local museums.
Day 10: Fly out of SFO back home