I agree that if the *only* reason you want to do an UnDisney day is so you do not waste a hopper day, then you can still do a disney related day! And my guess is this will be the kid's preference, too since they will be very eager to begin their Disney experience!
Dinner at one of the non-theme park hotels is your best bet. Chef Mickey's is an excellent suggestion; you may also want to try one of the Rainforest Cafes (My kids fave). One is in DD and the other at AK, but accessible to people not visiting the park that day.
A spin around the monorail is a must! My kids also love to just drive around WDW and see all the signs (some of them are very entertaining) as well as whatever sites they can see.
That is probably going to be your cheapest option! Well, actually--another option would be just to relax by the hotel pool, which is something that THRILLS my kids. Maybe just order a pizza delivered, and then go over your next day at Disney. Which park first? What rides does each member of your party most want to go on? Is there anything they are scared of? Which Character do you think you'll see first? What ride do you think will have the shortest line? the longest? That kind of stuff.
And finally--if you want a totally undisney day, then there are plenty of things to keep you busy around Orlando, although bear in mind they will still cost you $ (just not a day on your passes!) the Ripley's museum is good for an hour or 2, or you could also try wonderworks (
www.wonderworksonline.com ), which offers some really interesting interactive exhibits. They also offer laser tag pretty cheaply ($6 per person) as well as a magic show dinner. You can purchase a combo ticket to include 2 of those options, or a super combo including all 3 for about $25-30 per person.
Susanne