There is definitely an advantage to conducting the interview at your first choice school, and letting that school know it is your first choice.
Interviewers may or not follow up with the interviewee after the interview. The amount of follow up will probably be related to the likelihood that you will get accepted to that school, chooses that school, and/or get the Army ROTC Scholarship. If you have made it clear that your first choice school is Western U, do not expect much follow up from the interviewer at Eastern U. If you made it clear that Eastern U is your first choice, that interviewer is more likely to track your application, inform you when deadlines are approaching, and let you know if your file is missing information.
If you interview at Eastern U, the interviewer will be unable to answer any of the difficult questions you have about the Western U program. "Is it possible to double major in Mid East Studies and Arabic ? Does Western U give academic credit for ROTC classes ? Does Western U give a discount on housing to ROTC Cadets ?" The answer will be something along the lines of "I don't know. Call Western U." When you call Western U the first thing they are likely to say is "Who are you again ?". Then they will give you the number for the Mid East Studies dept, the Foreign Language dept, the Bursar's Office, the Registrar's Office, and the Housing Office. Then will then expect you to make the calls and find out the answers. The Eastern U interviewer will know about the "secret" Alumni scholarships that are not on the school's website, but will not know about any of the scholarships at Western U.
Getting admitted to Western U might be as difficult as getting the ROTC Scholarship. The Eastern U interviewer will most likely not know anybody at Western U Admissions and will not be able to help you get in.
During my 4 years in ROTC, the only students to receive ROTC Scholarships at Marist College are students that interviewed with me at Marist College. Some of these recipients did not receive it from the National Board but rather from the On Campus Scholarship budget. By interviewing here, making repeated visits here, following up with phone calls, etc., they built up a relationship that put them at the front of the line for the On Campus Scholarships.