This is a rather fine map tool / experiment / visualisation.
It is called River Runner, and will allow you to follow the route taken by a rainfrop.
Make your raindrop fall anywhere within the contiguous United States and the website will work out the route it will take to the sea and the tributaries and rivers it will flow through. It will then take you along that route.
It's really rather good visually, and I am assume is also accurate.
Check out Sam Learner's other map projects.