We usually plan 1-3 days at WDW before we start our park tickets. It is so much better than hopping off the plane, and directly into the lines!
Downtown Disney is very nice if your kids like to shop. Plenty of Disney-themed stores, and food...I think it is a great way to ease into the Disney feeling...
A couple more suggestions...The Boardwalk resort is our personal favorite hang-out in the evening. We go over, and rent surrey bikes and ride around the lagoon past the Beach Yacht Club and Boardwalk. The shops are open fairly late, and the food is great like the atmosphere. You can see parts of Illuminations from there too.
The great thing about staying at the Poly is that you can grab a hammock on the beach and watch the water parade and the fireworks with the perfect view and a pina colada if you like! We also liked to ride the monorail or boats to the Floridian and enjoy the atmosphere there as well.
I know your kids are older, but we also like the character dinner at Chef Mickeys.
Have a great time!!