When it comes to traveling to destinations that require a lay over , one can definitely take advantage. Many airlines will infact give a better mileage redemtion offer, if you include a stop over. Instead of taking the connecting flight in a few hours, check if you can take the one in 4 or 5 days. Airlines calculate the value of the ticket based on the route treating the stop over as a secondary option since not as convenient as direct. You in the mean time get an extra stop and use a few less miles (and most likely you get to check out some exciting city!)
I visited a few cities using this method. I got on the bandwagon and utilized many of the major mileage programs including Alaska Air ( had a stop over in seattle on way to anchorage ) American Advantage (had a stopover in Tokyo on way to Honk Kong) also with American Advantage (stopover in Amsterdam on way to Capetown).
* for additional tips on how to add another stop to your itinerary, while utilizing less miles check out my trusted source milevalu.com