Hi Kimberly, thanks so much for asking me this question! Over my many visits to Walt Disney World, I have stayed on and off Disney property. I have to say, staying ON property is definitely worth it. First, you get
Extra Magic Hours, which means that each day a specific park is opened for a few extra hours either in the morning or at night,
just for Disney resort guests. Of course you are also closer to all the parks and in the case of the Magic Kingdom area resorts, that park is just a quick monorail or boat ride away, as is the case with Epcot resorts being withing walking or boat-ride distance to both Epcot and Disney's Hollywood Studios. There are different levels of Disney resorts - value, moderate, deluxe and home-away-from-home, so there really is something in every price range. I think staying on property definitely offers an extra level of magic to your Disney vacation.
Not knowing your family, I'm still confident there will be something for everyone to enjoy at both parks. In Epcot, my tweens love doing the Kim Possible missions, riding Soarin' and Test Track and checking out the Innoventions exhibits and the stores in all the World Showcase countries (especially Japan).
In Magic Kingdom, my 10 y/o daughter loves the "Mountains of Magic Kingdom" - Space Mountain, Big Thunder Mountain and Splash Mountain, and everyone loves going on Pirates of the Caribbean, Haunted Mansion, Buzz Lightyear's Space Ranger Spin and more!
If you've never been before, check out the Magic Kingdom and Epcot
pages and look at all the attractions there, so everyone can decide which ones they'd like to put on their 'must do' list.
I hope this helps and if you have any other questions about specific rides or hotels, come on back and ask. I'm happy to help!