You sure you don’t need to do FoP?? If it’s just about the long wait, keep checking for FP or rope drop, otherwise that’s fine I was just wondering.
Without FoP and Everest, the main things are Kilimanjaro Safaris and Na’vi River Journey. If it’s warm/hot, Kali is a priority as well. I would get FPs for Kilimanjaro, Na’vi, and Kali for mid-day (between 10:30am and 3pm). Don’t rush rope drop, most people will be headed to FoP. Sign up for Wilderness Explorers, you can play these through the park. Do the M&G and then Dinosaur. Then, take a moment to walk through the trail in Asia (blanking on the name right now) before watching the Nemo show. Eat breakfast. You should already be in Africa, walk through the trail there before Lion King show. I would stop for a bit of streetmosphere and then use FPs and eat lunch. After that, since you have little kids, you could go to the Boneyard and ride TriceraTop. Afterwards, watch the Up! show in Asia. Then take in some streetmosphere and walk through the Tree of Light trails and the Oasis before dinner. Get in standby for Rivers of Light, then watch the Awakenings before exploring Pandora at night.
Quite honestly, without FoP and EE, the day is pretty loose and unpacked. I struggled thinking of what to do while writing this because, honestly, there’s not a ton. This doesn’t mean that it’s a bad park - I love Animal Kingdom - just keep in mind that you SHOULD have time for FoP and EE, so why skip?