You should check out Disney's Boardwalk behind Epcot. Just take a boat from the France Pavillon. There you and your party can ride a surrey bike, play some boardwalk games and check out dueling piano players at Jellyrolls bar.
Or, if you are on a romantic trip go to Port Orleans or Fort Wilderness for a Horse and Carriage ride.
Look into the guided tours of the WDW parks. They offer some really neat ones and some are included in various travel packages. I highly recommend the Magic Behind Our Steam Trains tour.
Another tip (along the lines of what Pacha suggested) is to check out the decor and theming in places you normally wouldn't go.
Walk around Blizzard Beach (even if you don't want to go on any of the rides) or visit some of the hotels you don't stay at.
An hour at an All Star Hotel or Pop Century can produce some of the greatest photos of an entire trip!
Just as Sweetie mentioned, I love checking out other resorts on property. I'm partial to the Wilderness Lodge, so I recommend paying that hotel a visit. One afternoon I just walked around the WL with my camera and ended up with some gorgeous pictures. As a little connection - if you are interested in steam trains but can't take the tour, walk over to the Vacation Club Villas at the WL. Just off the lobby on the right is the Iron Spike room where two of Walt's backyard train pieces are on display. Very cool. Also, in the MK train station, there is the jukebox that takes quarters and plays nice, early 20th century music. Sometimes I go up there, pop in a quarter, sit on a bench and get immersed.
I hope you have a great time! Let us know how it went!
"All our dreams can come true.....if we have the courage to pursue them." - Walt Disney
Seeing the architecture of WDW is a must. I am not sure if they still do it, but Disney use to give a tour of numerous building's (hotel's, administration, fire station...etc) and the information shared about the structure's was fascinating. BTW...touring the hotel's was a lot easier pre-9/11. For good reasons, security has been 'beefed up' since, so you will want to make sure you have ID (a resort key is great) if you driving from place to place.
Blizzard Beach is a favorite.
Don't forget to play mini-golf...I think it is more fun to do this during the day.
And though some say they are too slow (it really is a matter of opinion), rent one of those little speed-boats that you see crisscrossing the Seven Seas Lagoon. I think they are fun and you get some great views of MK, AKL, GF and the Contemporary.