One thought is to utilize the MK hotels for breaks and even for meals to extend "downtime." Poly has some places to sit both on the first floor and the second and you can usually get a view of the castle. I've eaten at both Kona and Captain Cook's, and spent time just sitting close to the lobby or up by 'Ohana on second floor. Contempo has a large second floor area with open space couches and you can walk there from MK if you like, maybe pick one of their restaurants to graze at or have a full meal.
At MK we don't really sit inside, but there is the "alley" off of Main Street, right around Uptown Jewelers that has benches and a few tables. Also, as someone mentioned on top of the Railway station. Both places we go and grab a snack from Starbucks and just chill. Also in MK go to Big Top souvenirs and grab a snack and head out to the tables and chairs near there.
At EPCOT we do usually sit inside, or at least in the shade. As someone mentioned, if you head behind Club Cool, and go in the double doors, there's an area in there where there are couches and tables with chairs, the bathrooms are close, again we grab Starbucks and head there. Also Sunshine seasons seating area, grab a drink or food and hang out, there is also a "small" alcove with benches in the pavilion. In the countries; in Norway we head to the bakery and sit under their overhang. In America, go hang out and listen to the Voices of Liberty back in American Adventure, and stay as long as you like.
At AK we head to Nomad Lounge for a drink and perhaps a snack, they have indoor and outdoor seating and do have a lot of interesting non-alcoholic offerings if that's not your thing.
DHS This is the one park I don't really have a hangout spot for, except down by where Starring Rolls use to be. They still had the tables with umbrellas, so again grab a Starbucks and hang out.
Of course at most of these places, you can also just grab a water and chill, it doesn't have to be a food stop (except Nomad Lounge where ordering something is good form).