This is a subject that has been the subject of extensive discussion during past seasons (and even in between). The consensus has been that while an Amazing Race could start or finish anywhere in the U.S., it typically starts in Los Angeles and finishes anywhere. The primary reason I believe this happens is that the World Race Productions offices are in El Segundo, a suburb of LA. Having the start in the greater Los Angeles area allows WRP to not have to transport all of its staff to another city. The tradeoff is that LAX is the easiest first airport for any race to track, so teams starting a new season are frequently spotted there. The list of cities that mjriches2005 has offered above is virtually identical to lists that I have presented on RFF years ago.
It is in the arrival city that more variation can be expected. The Finish Line has been in Alaska for AR12 and Hawaii for AR14. I do not expect it to return to either state anytime soon. The prime West Coast locations (LA, SF, Seattle, Portland, Las Vegas, Phoenix) have been overused as areas for Amazing Race Finish Lines. The only cities other than those to have an Amazing Race finish Line are New York, Dallas/fort Worth, Chicago, Fort Lauderdale, NY state park near Buffalo and Niagra Falls and Denver. I would like to see serious consideration of Boston, Atlanta, New Orleans (but not during its 6 month summer), Houston (same), San Antonio, St. Louis, Pittsburgh, Cleveland, Detroit, Columbus, Indianapolis, Minneapolis, Oklahoma City, Albuquerque, and San Diego.
I expect we will see Boston, Atlanta and San Diego in either starting city or finishing city roles in the next few years.