I actually use two pieces of free (or somewhat free) software. In the planning stages I use a website called BatchGeo to copy and paste a full list of addresses. The reason I use this service is that it is extremely accurate and well designed so I can weed out any obvious locations I will not go to.
After I pick the ones I want, I paste the list into another website called Speedy Route. There are two downsides to this service. The first one is that it doesn't interpret data that doesn't match perfectly in the system the best (about a 10% poor choice rate that you fix BEFORE plotting). The second being that it gives you 5 uses in 24 hours for free. For most of shoppers, it should be plenty.
The final step for me is just taking a picture of the address list in its new order and plugging them in a few at a time.
I will admit there are a few steps in my process, but I don't pay a dime during it; plus after the initial spreadsheet setup, have sped up both my shop selection and route planning process.