Just came back from a 3-generation trip with parents in their late 60s. Dad's in better shape than me but has little patience for crowds and line-ups. Mom's not a walker and needs frequent rests. We made out pretty well by starting at park opening or close to it and going until the heat got to us in the mid to late afternoon, then going back for a swim.
I tried to intersperse times in the hot sun and walking with sitting down in shady or air-conditioned rides.
Since the OP mentioned taking his dad, here's some "senior guy" ideas.
Magic Kingdom
We rode the Liberty Belle steamboat (first time for us, we all liked it), explored Tom Sawyer Island, watched Country Bear Jamboree and the Tiki Room, he liked the Jungle Cruise during our 2005 trip, we all liked Mickey's Philharmagic show, we rode the Wedway peoplemover thing in Tomorrowland, rode Its a Small World, and of course the train. The surprise favourite, which he wanted to ride multiple times when the lines were short - Buzz Lightyear! He would never touch a computer game or arcade game but for some reason loves to see how high a score he can get on Buzz!!
Epcot
We broke this into two or three visits and did a few Future World things and a few countries in World Showcase each time. Both parents really enjoyed the Nemo ride and Turtle Talk, and of course Living with the Land ride. Dad was gung-ho for Test Track (anything with cars!) Don't recommend TT though for anyone with back or neck problems, there's some side-to-side jerky movement in the beginning that's hard on the bod. Surprisingly they both tried the green ("low-impact") version of Mission Space and apparently got a kick out of it. They also enjoyed the details in the British and Moroccan "villages" and sitting to enjoy some of the entertainment and talk to the workers from other countries.
MGM
Dad really liked the old cars on Sunset Blvd. and in the Stars and Cars parade. He liked the car stunt show and the Indiana Jones stunt show in our 2005 trip. Mom liked the Little Mermaid show and Fantasmic in our 2005 trip.
Animal Kingdom
This seems to be a very senior-friendly park - or at least until it gets hot! They enjoyed walking all around the Tree of Life to see the details and get photos. They also loved the parade - lots of shady places and places to sit on the path between Asia and Africa if you get there early.
On the Africa side, the Kilamanjaro Safari is great as long as the senior is okay with a rough, jerky ride (not good for someone with back or neck problems). They enjoyed the performers in the Dawa Bar area and the cool misting fans near the drum station.
They liked everything about the Asia side, from the Tibetan village by "Everest," the tigers on the walking trail, the details on the sign, and the nice quiet bird show in the cool shade. Both parents love Kali River Rapids (get fast passes early in the day so you can do it to cool off before you leave the park).
On the Dinosaur side of the park, the shows are about all that interested my folks. The new Nemo Musical is absolutely worth getting there 45 minutes early for because not only do you get to stand in a shaded lineup and wait in an air-conditioned room, it is a beautiful and funny performance unlike anything they've ever seen before - a bit of puppetry and Cirque de Soleil with a parenting parable, all in a half-hour show! They also enjoyed the Festival of the Lion King show in 2005.
Non-park stuff
Both parents really enjoyed our visits to several Deluxe resorts during our 2005 trip when we were on the dining plan. Visited (but did not eat) at Grand Floridian, just went over to see their Christmas decorations (and Dad admired their old car collection). They loved exploring the Wilderness Lodge and Polynesian before and after our meals there, and Coronado Springs.
Boat rides are always nice. This trip we rode the Magic Kingdom ferry and they ventured out on their own one day to the Boardwalk by taking a launch from the International Gateway at Epcot.
Windowshopping at Downtown Disney is something better suited for a morning rather than an evening, I found out the hard way - it was a zoo the Saturday night we went! They enjoyed seeing the
Lego sculputures and the displays inside World of Disney. It would be nice to take the boat trip from there to see the resorts at that end.
We didn't do it, but boating or fishing on the Seven Seas Lagoon would be a blast for an older fellow, if he doesn't protest you spending that much money
Hope that gives you some ideas!