Depending on how busy it is, what kind of park day you want to do, and how much time you have, it might be worth hopping over to the nearby resorts. For example, there are lots of quiet places outside around the grounds of the Contemporary, Polynesian, and Grand Floridian if you just want to sit on the bench and decompress. If the weather isn't great, the lobbies at each of the hotels are generally pretty quiet during the day and you can also walk around and window shop. The Contemporary has its convention floor (2 or 3 I think) between the main lobby and the concourse where all the restaurants and shops are, and if there isn't a convention it's usually really quiet with lots of seating.
At Epcot the Beach Club is right next door and a really easy walk. It has lots of seating on the beach which is really nice. Hollywood Studios isn't really super close to anything, but you can walk or talk the boat over to the Boardwalk and the other Epcot area resorts or the Skyliner over to the other connected hotels. Animal Kingdom isn't walking distance from anything, but it's a quick bus ride away from the Animal Kingdom Lodge, which also has a fairly quiet lobby, plus the outdoor deck where you can look at animals. If I remember correctly there are even some chairs you can sit on and watch the animals go by.