gaRCfield,

Take your friend shopping. Tell them that you feel bad and that you can't put a price on your friendship so let them order what they want.
Be prepare for the sticker shock. You may think what you did was only worth $X but when your friend presents the bill be prepared to pay more.

I know you feel bad and perhaps you realize you should not have flown a borrowed plane in the manner you did, but you should let your friend determine the damage. You may disagree with it, but that is how I would do it.

Alternatively, just ask him what he feels a fair amount of the cost would be and give him the cash.