Some basic, off-the-cuff thoughts:
Andover students do show signs of stress. Along with Exeter, has the largest enrollment. Both offer PG year which could be good or bad depending upon one’s view.
Andover offers easy access to Boston–which could be good or bad depending upon one’s perspective.
Deerfield is athletic. Beautiful & relaxing setting. Offers PG year.
Groton can be intense academically. Smallest enrollment of the super elite boarding schools.
Hotchkiss & SPS kids are nice. Friendly campus culture at both. Not sure if still accurate, but in the not too distant past, Hotchkiss had a lot of NYC / Conn. kids from Wall Street / Hedge Fund wealth.
St. Paul’s School has a gorgeous campus. 100% boarding. 50/50 male female. Saturday classes. Changed athletic league a few years ago. Left ISL. Competes with the largest boarding schools now (Andover, Exeter, Deerfield, Choate, etc.) instead of with ISL schools (such as St. Mark’s & Roxbury Latin).
Lawrenceville is interesting. Over the decades I have seen a bit of a love it or hate it, but mostly love it. Beautiful. Strong relationship with Princeton University. Do you prefer New Jersey or New England ? Competes with schools like Peddie, Wyoming Seminary, Mercersburg Academy, probably Blair Academy, etc. Offers PG year.
All offer outstanding academics.
Important to visit. Very important to attend revisit days after accepted as other parents & applicants are great sources for obsevations & insights about the various schools.
Although Exeter is not on your list, I think that it does offer the best setting / location, but maybe not the best college placement among this group of super elite prep boarding schools.
An important aspect to consider is whether or not 100% boarding population is important to you & your student.