If you have something metalic (ferromagnetic that is) to attach your GoPro to, there is nothing better that I know of than using rare earth magnets. An excellent source for these super-powerful magnets for a GoPro mount is a computer hard drive. Undo the screws on the outside with a Torx screwdriver (here’s a review of the set I use), then pry it open.
Edit 1/14/2017: Published a new version that doesn’t require taking apart a hard drive, and has a few other advantages, including a protective coating so as not to mar the surface it’s on (Ben, thx for the suggestion about the coating).
Once inside, you’ll see a lot of interesting parts, but buried somewhere in a corner is an extremely powerful magnet. You’ll have to pry this out as well. It sort of reminds me of getting the good meat out of a scallop, or maybe even a pearl out of an oyster. There’s a lot of waste, but the payoff is something quite uncommon, an unbelievably strong magnet.
As for how to use it with a GoPro quick-release adhesive mount, it’s quite simple. Place the magnet in the center of the adhesive mount and roughly trace it with a box-cutter or X-acto knife. Peel the middle of the backing off and press the magnet on firmly. I used a curved mount meant for a helmet, but the straight kind should work as well.
I show this type of mount used above on a milling machine, but the possibilities for use are endless. Automobiles are an obvious target, and I was even able to stick it on a backpack that I modified to have two metallic patches for magnet use. Even though these magnets are incredibly strong, a safety cable (some options from Amazon) is still a good idea.
For a different take on a GoPro magnet mount, check out this egg timer device with a built-in magnet. The magnet’s not as powerful as what you can get from a hard drive, but it seems to do the job, and it adds a neat rotation feature.