I agree with everyone about going to resorts to relax. When at the MK its easy to get to a lot of resorts. Take Monorail to either the Contempoary, GF, or Poly. What I would suggest is take a boat to FW and relax there. Its very quite there and there are tons of places you can just sit and relax. If you do decide to do this then make sure you have a map of FW because it can be large and intimidating if you've never been there before. I wouldn't suggest the Contempoary because it can be very loud and busy. The Grand Flordian and Poly are good because they have really nice white sand beaches (so does FW). You can also take a boat to the WL, thats another place that is nice and quite.As for actually places in MK, there are't many because the park is busy 90% of the time. A good place to rest is either in a show or on the Tomorrowland Transit Authority. You get a nice, relaxing tour of Tomorrowland and you can ride multiple times.
At EPCOT you can easily find benches throughout World Showcase that provide a nice place to sit. On my last vacation werested on the benches overlooking the water in Italy, it was a really nice break. ITs also very easy to get to the Beachclub, Boardwalk, Swan, Yacht Club, and Dolphin. The Beachclub and Yacht Club have really nice beaches you can relax on.
Its easy to get to the same hotels as EPCOT from DHS. Its hard to get to too many hotels from AK because you have to take buses to all of then from AK. I haven't visited DHS or AK in a few years so I'm not sure where to rest in the parks.
Also, taking buses from the resorts could get very stressful so if I was you I would try to avoid taking the buses to a resort.