You can see the hops (routers) that your packets pass through from your machine to a target Internet site with the traceroute command (for Windows, use tracert in DOS/command prompt window). The route can actually vary from packet to packet, test to test, and the reverse route (return path) may not be the same. There are several traceroute servers around the world that can show you the route back to your browser. Tom Dunigan at ORNL also has traceroute server at ORNL.
The NDT software (source and compiled programs) is available via the Internet2 Performance web site at www.internet2.edu/performance/ndt/download.html. You can also learn more about the NDT system by subscribing to the NDT user discussion or NDT announcement lists hosted by Internet2.