Well... Let's just get right to it!
Rock climbing
Classic Cars or Hot Rod night or construct one yourself!
Water sports- if the weather is right, get out on the water! Rent some jet skis and have a go at it!
Auto maintenance: Learn how to change the oil on your car together or teach her if you already know
Self defense class
Shooting range or Archery lesson
Hiking or cave exploring... okay maybe you have heard this one a million times but I LOVE IT. It's probably the best idea out there because it's cheap, it's not structured and you get the opportunity to discover new things all while in the great outdoors. Kids really do love and enjoy being outside and letting loose.
Mommy Daughter Camping. Check out your local Girl Scouts council if you are not a Girl Scout already. You still can camp there and in my opinion it's generally safer.
Geocaching
Take her to a game: baseball game, basketball game, hockey game....
Build something! Pinterest has an endless supply of DIY ideas. I especially love the plumbing pipe diy
Volunteer because making the world a better place is something we should all strive to do but most importantly a lesson to teach our daughters.