Going into an interview and stating that my wife already has a job offer in the city may indicate to HR stability.
Honestly ATP, I don't think HR really cares if your SO has job stability in any city they have bases. Since they may have to reassign your base due to closure, openings or any other reason that may occur during your employment there. From my experience, I seriously don't remember any interviewer at any 121 interview I've done asking me anything about my family(that's including the company I ended working at). Such is the industry.
Your probably better off just stating you'll go to any base, anywhere they have an opening. That's probably more likely to get you the job.