I have a great idea for a 14 girl for a day trip....how about "Canopie Lake Park" in southern NH .It isn't that expensive and it's family oriented !!! I brought my 2 kids there the summer before last and they were DS15 and DD8. They had rides for young and old and it's just a nice clean family park. Sometimes you can find coupons too, during the summer at Dunkin Donuts or McDonalds!
I agree with Meg&Minnie. Canobie Lake is a great little park that she would probably like. My kids always have a great time there.
http://www.canobie.com/
I looked at the website and noticed that rates have gone up this year but you can usually get discount coupons at local McDonalds.