Because the DDP is so popular, as is the eateries at WDW, yes, even for Buffets you have to make reservations... there have been reports of places taking walk ups - or even people calling from the park to ask for availabilty (getting adr's from their phone when turned down at guest relations

)
I'm also one that takes each park day then looks over the list of restaurants and make a plan...
so I'd plan Boma for the AK day (Rainforest Cafe is there, but its a chain, the Yak and Yeti gets mixed reviews, I ate at their counterservice and was underwhelmed - for lunch go to the CS Flame Tree BBQ!!
MK - CS Columbia Harbor House - just across from Haunted Mansion, eat upstairs, its quieter and its a great value... for a TS (as in sit down meal) I'd go to the Polynesian for Ohana or Kona Cafe at GF 1900 Park Fare gets good reviews, but thier Cafe gets better reviews - at Contemp either the ultra Cali Grill and see Wishes from above, or the new THE WAVE...
you really need to look at menus and decide
www.allears.net click on dining then on the left side is a list click and up pulls all the places for that area...
EPCOT - in the Land is Sunshine Season that has an amazing value for their counter service (just be sure to find the Bakery area as opposed to the desserts pre packaged!) or try Morocco for a surprising good place - all the countries have a sit down and most have a CS place (fast food) again, check menus!
HS - their counter service leaves a lot to be desired in most people's view - we skip ABC commissary, but its easy to find, and quite large, so its popular - I prefer Backlot Express - its between the exit of Indy and Star Tours, its just not always opened! Their sit down include Mama Melrose, Brown Derby, both get pretty good reviews.. the buffet Hollywood and VIne it depends - then the quirky places like Prime Time (I'm not into the meatloaf or the 50's) and Sci Fi -
Just know as many posters as their are , that's how many opinions there are!!
and also, consider the Dining Plan - from picking items from allears menu, but factor in, we share CS meals - DH and I will get a "Big Breakfast Combo" meal and split it, and a lunch CS meal we'll get a large combo and split it - we'll get a large soda, or ice tea and a free cup of ice, and share it - but that's how we make it work based on our eating habits -
I've read several breakdowns of the DDP vs OOP and I think it can be a toss up depending on the ages of your kids (since yours are in the "adult" category you probably do save more by doing OOP) and if you do Buffets -
factor in also that June is now considered "HOLIDAY PRICING" for buffets!!
Buffets that we like Crystal Palace Breakfast gets you in MK before rope drop Norway Princess Breakfast at EPCOT - well you get the idea!!
Have fun planning and good luck!