I think it's dieting law that you pig out on Amusement Park days.
Seriously though, unless you're going to Universal or Disney, a big place that has real restaraunts in addition to their park food stands, you're not going to find anything remotely healthy.
It's one day and one day isn't going to kill you. Going to the Amusement Park is all about having fun. Use that as an excuse to have a cheat day! It'll be awesome!!!
But, if you feel you MUST eat something healthy, if you get a burgre or a hot dog, either only eat half the bun or throw the whole bun out. This will be a good and healthy way to cut some serious carbs out your diet for the day.