It all depends on what admissions is looking for. If you are in a big school, that school might offer you a lot more opportunities to engage in many different activities that will impress the board. In a small school with little to do, you can also get to do things that aren't part of the school, but to say one or the other will give you an advantage, I don't think they admission really cares. Plus attending a school next to military installation will not in any way affect the outcome of your application and remember that there are some kids that live and attend schools on military bases, and some of their parents are high ranking officers. Many of whom still don't end up receiving appointments, even with the military history and connections in their families. vGood luck!!
I do think from an admissions point of view that they see you more competitive in such district, but honestly I don't think its worth it. I myself went to a small high school and community colleges and did just fine in getting in. I also think you can always find something to do in your community. Instead of being just active, I looked into simple leadership roles. Have you considered that the district that you are looking at may be competitive in terms of getting an appointment?
Big school vs small schools have their respective trade-offs. Ex: Big school may have more opportunities, but at a small school would be easier to play three sports and letter in all of them. What matters more than the size/opportunity of the school is how you will compete with the people in the congressional district.