My favorites:
At HS - the back streets. while people do go back there it is not normally crowded, there are benches scattered around. I've spent many a morning with a cup of tea from the book store just sitting on a bench and enjoying the quiet.
At Epcot - the mosiac room at Morocco, it's nice and cool in the summer and while there may be people who wonder through they rarely stop. The gardens in both Japan and China have little tucked away benches
At AK - this is a little harder but the trails through both of the walking trail spots have benches and little side walkways that people rarely take.
At MK - as others have said Tom Sawyers Island is great. The river boat is rarely crowded and especially inside there are lots of tucked away places. The little tucked away cul-de-sac on main street on the right side after the first set of shops (if walking toward the castle) is often quiet.
You can always leave the parks and go to the resorts, all the deluxe ones and the moderates have little hidden away areas that people rarely go to. From MK just take the ferry or monorail over to GF or the boat to WL, loads of places at both of those. From Epcot, exit through the International Gate and wander around the back side of Boardwalk, just stay away from the pool or inside of YC there is a great sunroom. From AK,take the bus to AKL, loads and loads of tucked away places there. From HS walk or boat to either YC or BW.