Have you visited the state with her? Might you describe yourself as a frequent visitor? Did you ever go to school in that state or live there, even for a summer?
Here's how you might approach it:
"My girlfriend is from [state] and I've visited frequently and stayed as long as [number] weeks/months. I could see us settling down and raising a family here [or, in place of "here" specify a specific city or geographic area within the state] someday so learning medicine in [state] would be a great start."