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Walk Along The Wall
While the Old Town isn't big, it can still sometimes be hard to find the super old nooks and crannies that are woven in between the McDonald's signs and magnet stores. One of the oldest spots in the city can be found while walking alongside the wall that wraps around the town. Don't bother paying to go up the actual wall (you only get to walk a tiny part of it and the vantage point isn't impressive,) so instead just follow it as it snakes through the edge of the city.

A Danish king began building the defenses in 1310, and by the 16th century it was more than a mile long. While you don't have to walk the whole thing, you will find nice pockets of dusty old buildings and cute cafes if you keep by it.