We have eaten our packed lunches on tom Sawyer island many times. There is a gazebo with tables that overlook the water. It is so nice and peaceful there and usually nobody else is there! We have also sat on the benches that line the walkway by the water in Frontierland. In Epcot, we have eaten on benches outside of Test track. We prefer to bring lunch in, not only to save money, but also because we get sick of eating junk food.
This year we have 12 people in our group

we have reservations at yak and yeti, raglan road, brown derby and bog currently. But also we will be taking sandwiches in on a few days (8 park days)
On the menu thus far...nutty bird sandwiches--homemade whole wheat bread, freshly cooked turkey, alfalfa sprouts sunflower seeds and a wee bit of cream cheese.
Roast beef, cooked up that morning. (Easy since my mom is 81 and is awake every day at 3:30!) horse radish from our garden, and on daves killer bread. (Buy some if you ever see it!!)
And turkey and cilantro wraps. With added sprouts, and whatever anyone wants that morning.
Any of these beat the counter service options at mk and mgm. Ak has barbecue and Epcot EVERYTHING!
We usually just have a seat on a bench or wall

if people are ordering salads or fries then we will go early or late and sit in a restaurant. (But we also travel off season) we have 2 80+ parents, and a special needs child in our party. One type one and one type two diabetic... So common sense and healthy choices are a must.
Eta sclepping is easy. 2
ecv's and a stroller as a medical device.