There are some places that military families hope they will be posted to in the US, as there are more amenities and facilities than at other bases.
San Antonio in Texas is much sought after by military families. A move to San Antonio is popular because the area has a fairly low unemployment rate and the schools are geared up to handle army kids. The city has some great residential areas and, as there are several bases in the region, there is a good chance that you could get to move here at some point.
Omaha in Nebraska is also a popular choice; again, this is thanks to a low unemployment rate. Add to this a lower cost of living than in most areas and you could find that this adds up to a prosperous place to live.
You might also consider Oklahoma City. It may not be your natural first choice but, like Omaha, it offers low unemployment and a lower cost of living. Here you are also within easy reach of places such as Austin in Texas.
A military move to Texas could be on the cards if you are posted to a base near Dallas. This city is known for having plenty of military-friendly schools and businesses and again it offers a relatively low unemployment rate, meaning that there are more opportunities in the area for military families.
Finally there is Rochester, New York. This may not be high on your list but it has the lowest unemployment of any city with a military bases and you are close enough to New York City to have a day out whenever you choose.