Hi, Vicki! Welcome to the Disney Parks Moms Panel.
There is one tour offered at the Walt Disney World Resort that does not require Theme Park admission, the Backstage Magic tour. This would be a fantastic activity for your non-park day, as the tour is seven hours long and takes you to all four Walt Disney World Resort Theme Parks. This tour is only available to Guests 16 years or older.
Another option for your non-park day would be to splash around at one of the Walt Disney World Resort Water Parks. You do need to purchase Water Park admission. My boys love Water Park day! We are usually ready to leave about midafternoon, and have a lazy evening at our hotel.
You can also head down to the Downtown Disney Area (very soon to be Disney Springs). Spend your day shopping and dining at some fantastic stores and restaurants. You can also catch a movie at AMC Movies or have some bowling fun at Splitsville Luxury Lanes. You could also see La Nouba by Cirque du Soleil. I haven't seen this show yet, but it is high on my 'Disney Bucket List'!
Of course, you could always spend the day at your Walt Disney World Resort hotel by the pool. My kids wouldn't complain about this option - they are always asking to spend time in the pool. You could also take the day and explore other Walt Disney World Resort hotels as well!
Wishing you a magical vacation, Vicki!
~Rachel