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I'm using ArcMap 10.1 and have a shape file of polygons of municipalities. I also have the coordinates of the centroids of the polygons (if I need to use them).
I want a column in my attributes table which gives me, for each polygon, the distance to one specific point (lat 37N long 16E). I've been fiddling around with the Proximity Toolbox (under Analysis Tools), but don't know where to enter the coordinates of the specific point.

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You cannot directly use a coordinate in the tools. You first need to create a layer. This can be done using the "make XY layer" tool (after creating a table with your coordinate, for instance in an excel sheet with one column for Latitude and one column for longitude).

Then you can use the spatial join or the near tool in order to have your distance. If you don't use the centroid, the closest point on the boundary of your polygon will be used.

Remark: if you work on a large area, be careful with the projection that you use, because it can distort the distance calculation.

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You could create a point layer using the coordinate you have, then use a spatial join. to use a spatial join (right-click on the polygon, go to 'joins and relates' then join... in the join dialog, select 'join layer based on spatial location' and set it to the option that joins attributes from the nearest point in the new layer you made from the coordinate you have. this option will put a distance column into the attribute table for each polygon to that point

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