Find an online list of countries, print it, tape it to the wall, and throw a dart at it. Go there. (Using a map won't work, too heavily weighted toward Russia, Canada, etc.)
There are only about a half-dozen countries that it is actually impractical (or illegal) to go to, and none are dangerous if you exercise reasonable caution and be friendly and never go outside your hotel at night.
Here;s another way to randomly choose a country. First, go to
http://www.random.org/integers/
and set it to choose 3 random integers, within the range 1 to 223. You might want to pick three, to give you some wiggle room, and then go to the one that suits you best.
Then go to
http://en.wikipedia.org/wiki/List_of..._by_population
and see what countries correspond to you randomly chosen numbers above.
(I got 30, 205 and 103, which are Tanzania, Faeroe Islands, and Jordan.)