We are in a rural area in a state with a small population, where there is not a culture of kids going to boarding school. But as forward-looking parents of what teachers repeatedly referred to as "an unusual student" (asynchronous in the extreme) it began to be clear at the end of the elementary years that, aside from homeschooling (which we've done on and off over the years), there were not going to be local options for high school, either public or private.
I had grown up as a scholarship student at prestigious (and expensive) independent schools and colleges, and had had friends who went off to boarding school "back in the day"—so I knew not to let finances (or lack thereof) stand in the way of widening the search beyond our local area.
When we started our search, the only schools we really had on our radar were the ACRONYM schools—remembered from my long-ago school years, and considered because our dc is a. As we delved into the process, our search broadened to schools that would offer the academic opportunities our dc needed and some additional EC criteria dc (and we) considered non-negotiable.
So far, so good! DC is now a freshman at a school that seems to be a perfect fit.