You can use this tool to pick your own random spots!
For the last several years I have choosen my vacations randomly. Specifically, I have used mathematical formulas to determine evenly distributed latitudes and longitudes on the surface of a sphere. (Yes, I know the earth is an oblate spheroid, but a sphere is a good enough approximation for this use.)
This site (specifically the 2002 Q1 trip to Aylesbury, England, UK) was featured on Savvy Traveler the weekend of June 14th 2002. I liked how the story came out. As my sister said "They actually managed to make you sound sane!"
Pictures and stories about each of the trips are below. The sites for the later vacations tend to be more fleshed out than the earlier ones. The map shows the location of each of the random vacations as yellow dots. I used to live at each of the three blue diamonds. Now I live at the red diamond.