I'd go for MMA or self-defence. I did some self-defence training for a several years (along with judo and some goju-ryu karate), and overall, even though it's not MMA fighting, it gave me enough knowledge for self-defence. Granted, I'm barely 6 feet to 6'1 and roughly 190 pounds (work out at home a decent amount although slacked off for a while). Boxing doesn't really teach you actual self-defence. It teaches you how to move on your feet and throw a fast, hard punch, however, in self-defence, you need far more than that, assuming you're not up against a complete weak retard. What if someone has a knife or is also trained in boxing and self-defence? Now, you've got a problem.
But, being 6'6, I think that alone would be a good way to make others think twice.