I will mention something else about the schools with a large day student population, and from your list, specifically AOF and Westminster, which are both in suburban (by CT standards) areas and draw heavily from the local neighborhoods. When you get up to a 20-25% day student level, I think the school atmosphere/culture seems to feel more like the local area and reflect its demographics. That may not be meaningful if you are from far away and aren't familiar with different towns, but it was a factor for us and my son. For applicants from outside the area, it is probably a matter of just determining what "feels right" (in addition to all other, more objective, factors), which is hard to do without visiting. If at all possible, I think visits (while school is in session) make a big difference. The brochures and web sites all look perfect, but it's so hard to really know without being there.
Gratitude may help, and remembering what a tremendous opportunity and privilege you have. There are thousands of applicants who would have been thrilled to go to Lawrenceville (or any other school) but did not get accepted at all, or did not receive adequate financial aid, not to mention the millions of kids for whom an exclusive boarding school or private school education of any kind isn't even a consideration. As a parent, I would have been vary uncomfortable paying the tuition bill in July if I didn't know my child was thrilled to be going where he is going. How do your parents feel about it?
@Golfgr8 - I wouldn't think there's anything wrong or inappropriate about questions about safety and security. Here in CT, after Newtown, school security has been a huge issue. There have been ongoing discussions about security at our school. I am not sure if I asked it anywhere, but I have wondered about campus security, as these schools are very open and accessible (except for those in CT that you can only reach by driving for hours on hilly, winding roads). I would think that the safety of your child is a valid concern.
Southwest also flies to Bradley airport (north of Hartford), which is a good base for Loomis, NMH, Choate and Western New England generally. It's a lot smaller and easier to get around the area than flying into Boston, rental car may be cheaper, etc. Good luck!