This is certainly a trick question. They undoubtedly have absolutely nothing in common.
Their climates couldn't be more dissimilar, in fact.
The rocks at Black Rock Beach are nothing like those on Mt. Fuji.
Point Pleasant Park has some nice trees, but none that look like they fell out of the scene where Black Riders are chasing Frodo and the other hobbits.
And, finally, I don't think there are any caves in Halifax, unless you count The Ovens to the west of the city. But those caves were man-sized, and slime- and ice-free. Child's play.
In fact, the only area in which I am willing to perhaps concede the wee-est, littlest link between Halifax and Mt. Fuji is in the inhabitants' impeccably fashionable rain-gear.
And in Halifax's defence, going from, say, Pizza Corner down to the waterfront isn't quite so murderous on the knees.
If this hasn't turned you off completely, you can view more (lots more!) Mt. Fuji photos here.