We often bring our own food and non-alcoholic drinks to the parks. We don't like counter service food, for the most part (although there are some decent choices in some places) and the quality of WDW food has fallen sharply in the past several years.
In EPCOT there are several places where you can enjoy your meal. The little seating area by the Rose and Crown is open to the public, as are the benches down by the water near the Rose and Crown. There are some lovely benches in the gardens there too.
Canada, as mentioned is quite nice. America has the open air tables, which are good, and have umbrellas for shade. Italy has the water area with benches, as does Germany.
In the MK, it's not as convenient, but sitting at a quick service, or counter service restaurant table is perfectly acceptable. You've paid to enter the park and use all of its amenities, regardless of whether or not you wish to subject yourself to the mediocre food.
AK has many nice choices, so you shouldn't have a problem there. DHS is the one park where I'm drawing a blank. Probably because we don't often visit there, and when we do, we don't stay long.
Anyway, enjoy yourselves, and have a good time with your carried in meals!