Can you recommend some free-hand mapping software?

Any good drawing software that includes both freehand raster and vector graphics capability should do the trick. Photoshop is the Rolls Royce of such programs, but comes with a Rolls Royce price tag. PaintShop Pro should do, and is about 1/10th of Photoshop’s price. Gimp is actually a free download and is a full featured program. Any of these will let you draw lines in any shape, close them (connect the tail ends) so they act like a object, then let you pour in colors to fill each “state” with its own color and turn the oceans and lakes blue. You can also put in circles for cities, and type in text identifying each city, lake, state, river, etc.

Sounds like a project that would let him develop a very valuable skill set. Definitely support him in it.

It looks like there’s a number of tools for creating maps for roleplaying games. I know that’s not exactly what he wants to do, but the tools will probably transfer well to what you’re describing.

Here’s one that looks insteresting

Campaign Cartographer and they have a quick video walking through making a map.

A second vote for GIMP.

I use it for all my photo and design needs, including fantasy maps.

Yeah, the thing about learning any of those full-featured raster/vector art programs is you can make maps, but you can do so much more. It will do the sort of stuff you see on slick, high end posters for upcoming movies, and the art top-notch websites are illustrated with.