For example, I would like to calculate a midpoint given latitude and longitude. Is there a Python package that already does this?
You could try Shapely, which is just a neat set of geographic tools. Off hand, I think something like this would work:
from shapely.geometry import MultiPoint
points = MultiPoint([(0.0, 0.0), (1.0, 1.0)])
print points.centroid #True centroid, not necessarily an existing point
Also, did you know there was a whole StackExchange site just for GIS software questions? GIS.StackExchange is really helpful.
Lastly, have you looked at ArcPy?
This is a library built up around ArcGIS by ESRI. Unfortunately, it requires a license. Lame. But if your project has corporate backing, it is an extremely flexible and powerful library for geographic problems.
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