Ooo, this is my kind of thread. I'm 42, and went with my 70's aged parents. We did some rides, but have just as much fun seeing shows and soaking up the atmosphere.
So I'll just point out some things in each park we enjoyed. Some might be technically "rides", but they're not roller coaster types or anything like that. Just "dark rides" where you go along in the car from room to room immersed in scenes.
Okay. This is going to be fun. *rubs hands together and grins*
Magic Kingdom:
- Main Street, USA:
* Trolley show (very "Disney" and very cool)
* Main St. Philharmonic (really talented musicians and lots of fun)
*Main St. Vehicles (in the morning, you can ride the trolley, a double-decker bus, a firetruck, etc. down Main St.)
*WDW Railroad (you can take a relaxing train ride all the way around the perimeter of Magic Kingdom)
- Tomorrowland:
* Carousel of Progress (revolving theater with animatronic show spanning the decades. Classic attraction.)
* Peoplemover ("2nd story" tram ride that takes you on a tour of Tomorrowland. Great views especially at night.)
- Fantasyland (all three of these might be for kids, but they get points for nostalgia):
* Mickey's Philharmagic (3D film featuring Donald Duck and the famous music of Disney's movies)
* Peter Pan's Flight ("Off to Neverland!" One of the most beloved and oldest rides. Get there early or get a FP+!)
* It's a Small World (because you aren't really at Disney if that song isn't stuck in your head! Another classic.)
- Liberty Square:
* Haunted Mansion (probably the best dark ride on property. So much fun. Might be a good FP+ use too.)
* Hall of Presidents (theater show with animatronics tracing through all U.S. Presidents. Another classic.)
* Liberty Belle riverboat (relaxing riverboat ride around the Rivers of America)
-Frontierland:
*Country Bear Jamboree (another classic that deserves more love, IMO! I adore the show! So cute and funny!)
-Adventureland:
*Jungle Cruise (outdoor boat safari with animatronic animals and corny puns. Also good to do at night.)
*Pirates of the Caribbean (indoor boat dark ride, fantastic animatronics and theming, a lot of fun. Consider FP+)
*Enchanted Tiki Room (you'll swear someone slipped you some recreational drugs at some point. Trippy show.)
-Festival of Fantasy Parade (runs from Frontierland through Liberty Square, past the castle and down Main St. Great!)
-Castle show (new one is called Mickey's Royal Friendship Faire, happens several times throughout the day)
-Wishes fireworks!
EPCOT:
-Future World:
* Spaceship Earth (classic dark ride, pretty cool)
* Listen to the Land (in Land pavillion, educational boat ride, really neat)
* The Seas pavillion aquarium (skip the lame Nemo ride, the aquarium is awesome)
-World Showcase (pretty much everything here is worth seeing, but I'll list some highlights)
* Gran Fiesta boat ride (inside the big pyramid, very neat atmosphere in this place and fun little ride)
* Reflections of China (360-degree film in China pavilion, you stand up through it)
* American Adventure (theater show tracing history of USA with film and animatronics, seated)
* Voices of Liberty (AMAZING vocal group, sometimes inside where above show is, sometimes on outdoor stage)
*Impressions de France (beautiful film in France pavillion, seated)
*IllumiNations: Reflections of Earth (EPCOT's fireworks show, has lasers and other stuff, great music, beautiful)
Animal Kingdom:
- Kilimanjaro Safari ("must do" when visiting this park. You'll see tons of animals. FP+ is a good idea)
- Pangani Forest Trail (if you like animals/zoos, take a stroll through this to see more animals)
- Maharajah Jungle Trek (another hike to see some animals including tigers)
- Flights of Wonder (covered outdoor amphitheater show with wonderful birds)
- Festival of the Lion King (FANTASTIC! Just do it! Maybe a FP+ option)
- Finding Nemo: The Musical (I haven't seen it, but I hear it's well-done and worth seeing.)
- Jungle Book: Alive with Magic (haven't seen it, but might be worth checking out)
Hollywood Studios (Disclaimer: I'm not sure what's still open and what's closed down due to construction)
- Indiana Jones Stunt Spectacular (covered outdoor amphitheater show, exciting and iconic)
- Beauty and the Beast (another covered outdoor amphitheater show, great if you love the movie)
- Great Movie Ride (lengthy dark ride through iconic movie scenes in the Chinese Theater)
- Launch Bay (if you like Star Wars, check it out. Stormtroopers patrolling around, can meet Chewy and Kylo Ren)
- Fantasmic! (nighttime spectacular in a huge open-air amphitheater, Mickey battling evil, fireworks)
- Star Wars: A Galactic Spectacular (I saw the earlier version "Symphony in the Stars" and was absolutely gobsmacked at how amazing these fireworks were. This is a new version that is different but supposedly still amazing.)
I'm sure there are many more things, but those are the things we either did or have heard are good. Lots to see and do without ever hitting "headliner" rides at WDW! Have fun!
Edited to add: If you want to see the best show on property and can work it into the budget, the Cirque du Soleil: La Nouba show at Disney Springs is hands down the most amazing live entertainment there. If you've seen Cirque shows before, it may not be as amazing to you, but it was my first and I was AMAZED! Thoroughly enjoyable!