Everything the others have said (Snow White's wishing well, entertainment) and I'll add getting a cup of coffee and nabbing a seat on the "front porch" on Main Street (halfway down on the right if you're facing the castle) to people watch. I also love wandering through the back alleys and shops in New Orleans Square, or just sitting along the riverfront.
The Disney Gallery is a fun place to visit (and cool off in the summertime) and there are no end of beautiful garden displays to enjoy all over the park.
I know these are rides, but the Mark Twain Riverboat and the train ride around the perimeter are also favorite ways to relax.
At California Adventure, see if you can find any of the "town residents" along the main street to interact with. Relax (even lie down) in Animation Studios and enjoy the "show" all around you on the walls. Take the long way around the park (past Grizzly River Run) or duck into the Grand Californian to relax by the fire. Go through the Boudin Sourdough bakery walkthrough and get a free piece of bread. Sit outside at Starbucks and watch people, or sit outside by the winery.
Don't miss the path from the Pacific wharf area to the back of Carsland (by Radiator Springs Racers) for some gorgeous views of the "Red Rocks" and fun "roadside signs."
Watch the "sunset" at the end of Hollywood Blvd at the picture spot.