When you fast travel, there is a chance that you will fight a dragon (I'm aiming for the kill a legendary dragon achievement, I am level 78), but I'm wondering, is there any location that has the greatest chance of spawning a dragon? Like, do towns like winterhold have a greater chance at spwaning a legendary rather than say, FT to a random cave?

EDIT: At 4:38 PM on the 20th of First Seed, Year 203 in the 4th Era. The Dovahkiiin fought and slayed his first legendary dragon.

FTing to a town or city will increase Dragon and Vampire attacks.

I've found that Dawnstar and Winterhold are Dragon magnets.

You could also go to the various lairs and try your luck.

I went to three lairs. Found a regular, blood, and ancient dragon. No Legend.

There is also Morthal

The chance are somewhat remote that the dragon you end up encountering will be a Legendary Dragon, but what others have said about the unwalled cities/towns seems to be true. These include Falkreath, Riverwood, Morthal, Dawnstar, and Winterhold, because there are one or more random encounter spawn points nearby each of these towns. When I encounter a Legendary Dragon, it is usually in the wilderness or along a road. Fast traveling doesn't seem to always be the solution to finding a Legendary Dragon either.

Well, I just need to find it once for the achievement.

I would recommend visiting the dragon lairs until you find one, you may not be able to collect it's soul however, perhaps dampening the moment of your first legendary kill.

Mine was outside of Morthal, but away from the city itself, in the marshes by the abandoned shack. In that area. They will catch you when you least expect it, usually when you are busy fighting off something else. And believe me when I say you better have plenty of potions, and save just before the fight. I was glad I did.

A Legendary Dragon also attacked me outside Riften on the road to Snow-Shod farm.

Have you also tried Arcwind Point?

Arcwind Point did the trick. There was a texture glitch, but a nice amount of gold and a daedric helm. And the achievement of course