The first time we went to Disney (in 2005), my kids were 7 and 9. At the end of the trip, they said Epcot was their favourite park.
Here's what we did...
Purchased passports for each of them. They went to every country, stopped at the KidCot craft stations and got a stamp. Then they asked the castmembers to write "hello" in their passports, and they practiced saying hello in their language. Made a lot of new friends!
Did everything they could in Innoventions, which at the time was some sort of "Fire Safety" thing, paper making, and a city energy planning game. For whatever reason, they loved it. Plus, the castmember in charge of the Fire Safety exhibit gave them a certificate for completing the activity. I think the only thing currently in Innoventions is "Colortopia"? Still, that is also fun, even for us adults (we tried it last time we were there).
Made sure to arrange our time so we could see some of the shows and demonstrations (ie, feeding the manatees in The Seas, belly dancing demo in the World Showcase, etc). Spent a lot of time looking at exhibits and talking to castmembers, and getting to touch things like shark teeth.
On a subsequent trip, my daughter spent a good hour playing with the "Virtual Surgery" thing in the post-show area of Spaceship Earth.
For us, at Epcot, the rides were almost an afterthought. It seemed more like a large, sprawling museum. Which, as enormous museum geeks, was right up my kids' alley.
If I had a six year old these days, I likely would do Epcot, because I think we'd have a heck of a lot of fun with the passport. Plus, I'd do whatever the current scavenger hunt is (Agent P?). But I also think it's completely reasonable to want to skip it, if these things aren't your idea of fun.