I've had filet at least once at every WDW restaurant that serves it except the Brown Derby.
Kona--It's "OK" but there's a LOT of better places to get filet. Kona does have EXCELLENT food, but filet is not a specialty of the house.
Narcooses--See Kona, and we've had service issues there several times. Not sure when or if we'll bother going back due to the service.
Citrico's--Has a great filet, but again there are other menu items while they excel in. It's also a more sophisticated and upscale restaurant with a dress code, so probably nto right for the OP.
Concourse Steakhouse--We had good but nothing special filet there. However it might be an option for you, it's kid friendly and casual, and a short, easy walk from the MK.
California Grill--I've had some pretty good filet here. It's upscale and has a dress code, and is probably not what you are looking for.
Artists Point--They ruined my filet by overcooking it terribly, I actually sent it back, it came out a second time still over cooked. Other items there are great, but not sure I'll order filet there ever again.
Yachtsmans Steakhouse--Has recovered from a major decline a few years back and has very good food. It also has a dress code and is not a place you'd tromp into right from a park.
Shula's--We had excellent steak there, but it's not inexpensive, and by not offering a kids menu, charging a meal splitting fee, and offering free kids care at the Dolphin Kids Club they make it clear in so many words that kids aren't exactly welcome. They also have a dress code.
Le Cellier--We've had filets that ranged from good to excellent here. IT's casual and kid friendly, and is right in Epcot. It's probably going to be your best bet.
Bistro de Paris--This is also in Epcot but offers upscale dining with a dress code and no kids menu. My filet was OK, but far from the best I've had.
Jiko--This is the best filet meal I've ever had anywhere. It's simply incredible. It's also an upscale restaurant with a dress code.
Bottom line, I think le Cellier is going to be your best bet.
Anne