Daytime:
Just hang out at the resort and pool. Haven't I seen you posting on the DVC board? So if you are DVC members, if they aren't crowded, you can pool hop to most of the other resorts.
Go check out the other resorts. Actually I like to do this in the evenings too. Go to the other resorts and walk around the different lakes, etc.
Not sure if "those that don't involve the parks" includes the water parks but they can be fun and relaxing.
Golf (many beautiful courses) / tennis / etc. (Mini golf at Fantasia Gardens or Winter Summerland) Golf and tennis lessons available
According to the time of year, the Braves have spring training at the Disney Wide World of Sports Complex. Also at the Sports Complex is the NFL Experience.
Richard Petty Driving Experience.
Sammy Duvall's Watersports Center at the Contemporary Resort.
I know you said no parks but Disney offers a list of tours that are usually around the parks but involve so much more than the standard attractions.
Day at the spa.
Fishing.
Boat (Sailboat, WaterMouse, canoe, kayak, pedalboat or pontoon according to where) and bike rentals.
Surfing at Typhoon Lagoon with instrution (Craig Carroll's Surfing School)
Disney's Dolphins In Depth (no scuba cert. required) or Dive Quest if you are certified.
Horseback riding.
Evening:
There is Pleasure Island. It has a little bit for everyone. There are the traditional clubs with all different types of music and dancing. There is the Comedy Club. One of my favorites it the Adventurer's Club (sort of like being in the middle of a skit and a lot of fun).
Cirque du Soleil at Downtown West Side.
The list of fine restaurants at the parks, downtown and resorts could go on and on.
The Boardwalk with ESPN Club, Jelly Rolls and Atlantic Dance in addition to a long list of excellent places to eat.
Hoop-Dee-Doo Musical Review.
Numerous different lounges at the resorts, many with entertainment on various nights.
Illuminations and MK fireworks cruises.