I agree with Pedler. If you have enough days already, adding one more is only a few dollar extra, of course you can always add an extra day on to your ticket if you want to once you get there - you just have to add the extra day before the original 14 are up. You can also add the no exp. option, too. At 4 pm...exploring AKL is a fun thing to do (remember, they have that storyteller at the fire), Downtown Disney is a fun thing to do, Disney Quest is a fun thing to do (Esp. for the guys), you might consider PI if you are all adults, and there is the Boardwalk, too. It also depends on the park hours at the time of your visit - if it is an EMH night for one of the parks, I'd go to that park. If not, going into the World Showcase at Epcot is another great idea, and it feels wonderfully decadent to go in just for a dinner (dinner, the Norway ride, and Illuminations). I'm not a heavy drinker, but treating myself to a single fruity cocktail before dinner the first night is a real pleasure - and a way to signal that hey, I'm on vacation! So if you decide that you aren't up for a park - just having a cocktail (and it doesn't even have to have alcohol) by the pool while the kids swim before a nice relaxed dinner is a nice, relatively inexpensive way to start a vacation. Of course you could also go resort hopping, too - Make a PS for dinner at another hotel, then go early to explore. If you go to the Poly, GF, Contemp. or WL, you could maybe see the electric water pageant that night, too - and it is free.
Also, if you are only going to Disney, and you will have a car, the first night is also a good night to explore Orlando - I-Drive is something to see!