Stein heads out from the Citadel of the Green Star in the indicated northeast direction. He's already been this way before, kind of. He's heading in the direction of the mountains to the north and thus to the lake of lava on the other side of the mountains.

He doesn't recall having seen any tower anywhere in that direction before, but his route was on the ground, and, depending on how high the tower was, it could have easily been hidden behind any of the foothills or tucked into one of the narrow valleys of the mountains.

As was suggested by the others, the direction might not be absolute but simply an arc of the compass. If that's the case, then the farther away from the Citadel he went, the wider the area would become that had to be searched.

In reply to GM StarMaster (msg # 1):

Naturally, given the hills, Stein would take to the high places for visibility, to see through the valley and try to spot the top of any tower. After all, the idea was that a tower was, in fact, a tower.

however, a tower is usually looming and obvious, he himself said that these places seemed to be trying to use being hidden as their prime means of security. So as they traveled they would direct a few insects to sweep under the canopy, the lower lands, to wident the search to maybe find some kind of small, or perhaps inverted, tower.

but all and all, that was the aim, find the tower. it was suppose to be in this direct but the information proveded suggested a limit on how far out it was.

also, given that the hats name was fade away, it was assumed that the magics involved would be invisibility and so throughout this search Stein would use detect magic.