You're right, it wasn't too difficult to guess the location without the stars. The base did happen to be right in-between the 34 and 35 degree lines (34.6 lat), and you can estimate pretty well with only one line
Little Rock AFB is a few tens of km north (34.9 deg lat) for what it's worth. There may be some others as well. The chances of getting a picture of the stars that clear in Arkansas is way lower than in the Mojave however...
Considering Little Rock is a C130 airlift base it's pretty easy to rule that out without looking at stars.