What's the best approach towards building up a Route Planner system?

I work as a volunteer for a charity and the volunteer coordinator knows I do little bit of programming every now and then. However, after I located a bit of web service API coding to use in Microsoft Excel / VB Macro to get the distance from postcode to postcode for the mileage and so he has come up with a thought it might be valuable to try and figure out a way to tin collection route planner - so basically leaving from the office to collecting tins on the list we have and then coming back to the office with the shortest routes available and showing a map / directions to get there and back in which would save staff valuable time.

I'm struggling to find a reliable source / one that could be used in how the volunteer coordinator hopes I can achieve - there are some sites that seems good but then the pricing is still limited in terms of API requests - even Google Maps has it limitations with only allowing 23 (including starting and finishing point) waypoints.

Anyone done a similar sort of concept or can provide some sort of approach that I can use with Visual Basic for Microsoft Excel or PHP or something on those lines to help me pursue this idea please - many thanks in advance. :)