DS has a lot of faculty kids at his school, but there are a few who have bucked the trend to go somewhere very different (and of course, all the girls go elsewhere). I can imagine faculty kids feeling a bit claustrophobic going to school where they have grown up and where their parents work.
As far as looking outside the region, we had no prior BS history (such as family tradition), but there was no reason to look farther than CT/MA — once we added BS to the secondary school mix, we had ample options. For families in NYC the ease of transportation makes a bigger radius easier, having pretty easy access to both NE and Mid-Atlantic (PA, NJ, MD, VA). Plus, the secondary school advisor at my kids’ school was familiar with some Mid-Atlantic and CA schools but not nearly to the same degree. I know of one kid going to CA (Cate) in the years my kids attended.)
And yes, we are lucky to be close as we get to see games, and it has worked out for DS to play his club sport. If he were farther away and less accessible, his trajectory might be very different.