Well to build strength (in a resonable amount of time) hiking and climbing aren't going to cut it... (Neither is what you're thinking of, perv
)
I'd say the gym is the best place. It's a controlled environment (kinda).
But with your busy schedule, it's going to be hard to fit in 3 or 4 weekly visits to the gym.
Alternatively you can do some exercises at home, using your body wieght instead of dumbells.
Before you know it, you'll be throwing chicks from one side of the bed to the other, lifting them up in dark alleyways and stuff like that....
(what, you think I work out for fun?? )