Spend the money on the right bike for your kid. Get the best one you can afford. They will always remember such acts representing how much they mean to you.

My daughter rides the Huffy she won through the school but I've gone through that one as best I can. She doesn't ride too much but she's also of a strong mind. (That's her bike and she's going to ride it! she tells me)

My son rides the Giant Boulder I won but when the mood suits him he takes my Bianchi Milano. He doesn't like my OCR3 but he likes the liquid black color it is.

Believe it or not, kids have a pretty good idea what a certain bike is worth. If it's a good one or it isn't. Find a great bike. Whether it's new or it isn't should matter less than its overall quality.

Best to you,
Harv