R is free & open source, and widely used for stats, data manipulation, analysis and plots. You can get geographical boundary data from GADM in RData format, and use R packages such as sp to produce charts easily.

Or at least, as easily as you can do anything in R. I hesitate to suggest it to people who already do data work in Python (it's less ... clean) but in this sort of domain it can do many things easily that are much harder or less commonly done in Python. My impression is the really whizzy, clever stats/graphics stuff is still all about R. (See e.g. this geographic example.) There are many tutorials, some of them very good in parts, but it's famously slippery to get to grips with.

More on spatial data in R. You can also get a long way with the maps and mapdata packages.