in MK, our favorite 'resting spot' is riding the TTA. We get on, ride a few consecutive times (the ride operator will usually let you stay on because there is rarely a line) and ride it around three or four times.
In Epcot, we like to rest in the American Adventure. Sit on a bench in the lobby and relax until the show starts, then sit and watch the show in the air conditioning. Ditto with Ellens Energy Adventure.
Yup.
Also in Epcot:
Spaceship Earth
Impressions de France (film in France) Guests are seated, unlike in Canada or China.
Boat ride across WS Lagoon (near Mexico or Canada, Morocco or Germany.) Not a long ride, but scenic & relaxing.
Lots of longer shows at DHS:
Beauty and the Beast (30 min.)
Indiana Jones Stunt Show (30 min.)
Lights, Motors, ACTION! Stunt Show (35 min.)
Great Movie Ride (20 min.)
Muppetvision 3D (17 min.)
Voyage of the Little Mermaid (15 min.)
Lots of longer shows at DAK:
Festival of the Lion King (30 min.)
Flights of Wonder (25 min.)
Finding Nemo the Musical (40+ min.)
Kilimanjaro Safari (18 min.) Although this one's a bit BUMPY!
Places just outside the parks (you may exit and reenter the same park at any time.)
From MK, I suggest taking a nice (free) boat-ride over to Ft. Wilderness and enjoy the quiet areas with grass or the sandy "beach" areas.
Anyone can visit any of the resorts and FtW is a great place to relax.
From DHS' front gate or Epcot's International Gateway between "UK" and "France," exit and take a nice (free) boat-ride over to the Yacht and Beach Club resorts. There are nice beaches there (on the lake, not the pool) with chairs.
At Animal Kingdom, its very quiet and there are lots of benches over in the "Rafiki's Planet Watch" area.
You ride a train from/to "Africa" to get there and back.
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