Unless you're staying onsite at WDW, you should avoid each park on its 'early entry' day. (If you don't already know, Disney allows its resort guests into a nominated park each day one hour ahead of regular park guests). The current schedule is:
MK - Sun, Thu
Epcot - Wed
MGM - Tue, Sat
AK - Mon, Fri
The time of year you are visiting obviously has an impact on crowds in general, but doesn't affect this premise - the single best crowd avoidance tactic in my view. Even if you're staying onsite and want to take advantage of the extra hour to get a few of the major attractions under your belt, the consensus seems to be that you should 'hop' to another park around mid-morning when the crowds at the early entry park start to build up.
A popular strategy for AK is to head straight to Kilimanjaro Safaris (probably the most popular ride) as soon as the park opens for two reasons - you beat the lines which will inevitably build up later in the day (although FASTPASS is available) and you will potentially see more animals as they are more likely to be out and alert early in the morning than later in the day when the heat is greater. I have to say that we've done KS at various times of day and I've never noticed a difference.
Other 'not to be missed' attractions are:
It's Tough to be a Bug! A great show in itself, but it also allows you to get a close-up view of the Tree of Life;
Festival of the Lion King;
Dinosaur;
Kali River Rapids.
All that said, there is so much more to AK than the theme park attractions and it is so easy to pass it all by. We enjoy getting to the park early and heading out towards Asia whilst everyone else is rushing off to KS. There are loads of little trails to explore and 'secrets' to discover and you'll have them to yourselves at that time of day. Maharajah Jungle Trek and Pangani Forest Exploration Trail are also well worth setting aside some time for. I'm sure the children would also enjoy the petting farm at Rafiki's Planet Watch and the Pocahontas show at Camp Minnie-Mickey.
