Bill Cook, mentioned in this post, has written an excellent and entertaining book on the TSP that is accessible to non-experts: http://www.amazon.com/Pursuit-Traveling-Salesman-Mathematics...

If you're not interested in reading an entire book on the topic, Cook's webpage provides a summary and includes several examples: http://www.math.uwaterloo.ca/tsp/

Finally, here's a simple version of the TSP showing route optimization in San Francisco using local businesses: https://forio.com/app/showcase/route-optimizer/