So, I stumbled into a pretty nifty website called Inkarnate. They've got a beta-ready web app for drawing world maps, so I went ahead and gave it a try. Below is my second attempt, the first try being a practice run.
I'm pretty happy with the way it turned out.
There are some pretty good tutorials on YouTube for the app, which helped me get up and running quickly.
My verdict: two thumbs up! I will come back to this app and check on their progress, as they have more features that they want to add (and that I want to use).