Ride the bus to AKL and look at the animals from the public viewing area, watch the fireworks and or castle light up from the 14th or is the 15th floor of the Contemporary. You can also see the water parade if you time it right. You can also walk along the beach at the GF or stroll the nature trails at some of the resorts.
We love exploring other resorts, and visiting the town of Celebration. It is really beautiful.
We even did the DVC thing one Sunday and since it was during luch time they gave us vouchers for a free meal at one of the resturants on the Boradwalk.
We love to walk along the Boardwalk and Downtown Disney as well.
We even have a sort of ritual where we go to Epcot through the front gate and pay for our admission, walk through the world showcase and exit out through the international gateway to tour the boardwalk. If you leave within a one hour time frame you can get refunded your admission. I think you can do this at other parks as well, but I have never tried it. We do it because I like to shop at Germany and France. When my kids are a little older we are planning a day trip. I think they call this a shopping pass or something like that, but you do have to pay to get in initially.
My kids love to ride the monorail and look for hidden Mickeys at the resorts as well. It is sort of a scavenger hunt kind of thing.
Sam