I went to Universal last week with my 4.5 & 1 year-olds. Because I didn't see any threads in /r/daddit when we were planning I thought I would add my own afterwards.

Stroller/walking: We walked ~6 miles each day for about 3/4ths of a full day at the park both days. We bought a second-hand double-stroller just for the trip and it fit everywhere in the park and could be stashed on the shuttle bus fairly easily. If your stroller doesn't have a zero turn radius, it will probably not easily maneuver through some key areas. You can rent strollers at the park. I would definitely recommend a stroller for kids that aren't old enough for that amount of walking.

Height: Kids over 40" can ride most everything they would be interested in, including a couple roller coasters, which were great first coasters for my 4 yo. Over 42" opens up a few more.

Harry Potter: The Harry Potter areas of the park were easily the most crowded, so shoot for those in the early hours of the morning. The interactive wand is expensive but probably worth it for a young HP fan. Several of the interactive areas weren't working well. I could see it being disappointing for an older kid who can see through the "magic".

Child swap: Many rides have "child swap" which is easily the greatest thing in the park. You take your too-young or unwilling kids through the lines together and your partner or older kids get to ride while you stay with the younger kids and then you get a turn immediately after they are done.

Lines: A few rides have a virtual line where you can jump to the front at a specific time...but there's so few that I didn't do it. The express pass gets you in a much shorter line, but at this time of year (late April) it wasn't really needed. Off-peak season is definitely the time to go if you can swing it.

Little kid areas: The Dr. Seuss and the Curious George areas were great home bases for young kids. There was basically zero wait and plenty of rides for little kids.

3D/4D simulator rides: The Jimmy Fallon ride was cheesy but good for my 4 yo. The Minion ride was similar. My 4 yo closed his eyes through the entirety of Spiderman, but he didn't cry about it...it was just too loud/overwhelming. Simpsons was similar.

Coasters/flyers: Pteranodon was fun for both parent and kid and it was great to use it as "this is what the coasters are like" because there's just enough speed and turning to get the fun across to a timid kid. The Woody Woodpecker was his first real coaster and it's pretty tame...just do your best not to crush your kid. After it my kid was ready for the Hippogriff, which he was scared of the previous day.

Hogwarts Express: You need the park-to-park tickets to take it and it's really worth it even if you don't care about Harry Potter, just so you have the flexibility of making a loop through both parks.

Food: You can bring in "kid food" and snacks, but otherwise plan on eating inside. Both of the Harry Potter restaurants were pretty good and easy/fun and not crazy expensive. You cannot refill water bottles at the Coke stations without paying for the refillable bottle. You can refill your own bottle at water fountains (not cold) or any food service/bartender will do it for free (cold water).