We don't tend to do very many entire non park onsite days, except arrival/departure days. One thing we'd do with a non-park day is to rest, so we could tour harder on our park days. We'd probably take time for some table service meals, and especially take time to visit Disney Springs, and ride around via the shuttle boats/Skyliner.
Our non-park days tend to be offsite (split stays) with a car. I usually find that all told, renting a car saves us money. Having a car means we can eat a meal or two offsite, so better food for less $ than eating onsite. It is possible to rent a car for just a day, but the price is often the same for a full week.
A REALLY great option that opens up when you have a car is to drive to a FL or national state park. There are tons of options, and they are practically free to visit. FL is home to many natural springs, wetlands, beaches, historic sites, etc.
If you have never ventured to St Augustine, it is a place everyone should visit. The fort is amazing. Clearwater beach is also doable as a day trip. Even better are the beaches of Honeymoon Island. There you can see all sorts of wildlife and find tons of shells. The Gulf coast beaches are all very calm. The Atlantic beaches have bigger waves.
Closer to WDW, is a day trip up through Ocala NP and Silver Springs State Park. The glass bottom boats tour is a ton of fun, and really unique. You can also rent a kayak if you want a close up view of the wildlife.
If you have never seen the Everglades/Big Cypress that is another must-do, IMO. You can tour much of the Everglades NP area by car. Closer to WDW are other options to take an airboat tour, and see a small northern part of the Everglades if you don't want to drive very far.
Very close to WDW is Celebration and the outlet malls. Celebration is just a pretty town, but it has some nice places to eat. You could also easily visit Citywalk at Universal.
