Mapping: calculate distances between all points in two data sets

I need a mapping tool that provides a specific use case. Maybe you are a GIS expert, a developer, or simply know the answer! I'd prefer to use an existing tool than develop a new one; but would consider development if there isn't an off-the-shelf solution. I have set a relatively low budget here simply to find existing tools.

My use case:
1) I have a list of locations for all my posters (billboards) {location set A}.
2) My clients often provide a list of locations of all their stores {location set B}.
3) I need to be able to calculate the distance between each location in set A, and every location in set B.
4) Then analyse the results (e.g. "show me all posters within 500m of a client's store").

I can find
1) Lots of tools that will calculate the distance from a single point to multiple other points.
2) Code for calculating the distance between two single points.
3) Data processing tools to analyse the outcome (I could even do it in Excel).

I can't find a single tool that makes the calculations I need. I know that other companies do this - can you source a suitable tool?