@Steve DellaPelle Agreed with all the feedback given so far. One important item that you should first figure out is your risk/return ratio. How much risk are you willing to take for what amount of return? The higher the risk, the more return you can achieve with any investment, including real estate investment.
San Francisco, New York, Boston,...are considered to be 'safe' cities with long-term appreciation and relatively low risk. These cities will not have a high rental return though (but appreciation will be/should be there). This is because they are large metropolitan areas with diverse industries, attracting many people to work and live there, etc.
Other cities such as Detroit, Houston, Dallas, .... also offer some interesting investment options as the rental yield can be higher (compared to some of the coastal cities) but then you may have to consider issues such as decline of population, less diverse industries, more land available,....
As such, determine your budget and risk/return profile - that should help you greatly in narrowing down to a few cities. Good luck!