I have always been a big fan of stopovers. Most airlines will also give you one on FF-award tickets, don't forget. A favorite combination I used to do on Delta was to see a city in mid-America like Kansas City (with LOW weekend hotel and car rates) as a stopover to Las Vegas, where the low costs are during the week.

Airlines won't volunteer the info about stopovers, though. You have to propose something specific to get them to work with you on booking the award trips.