My vote is for Hanover NH to one of the White Mountain notches (Franconia, Crawford, or Pinkham), depending on your pace and interests / abilities.
This hike meets the stated criteria, is reasonably accessible, starts off moderate and becomes increasingly more strenuous as you go along (commensurate with scenery).
Of course the Whites are popular, but then what part of the AT worth pursuing in August isn’t popular?
As an easier alternative you could hike the AT where it follows the Long Trail in Vermont, from the MA / VT border as far north as you have time for. Not nearly as much bang for your buck, though, imo. Nice forest, occasional views.
The AT in Mass and Connecticut is lower overall, and you could easily hit a heat wave in August with 90 degree temperatures or better.
Maine is another option, but quite a bit more remote in terms of access, and the terrain can be extreme (interspersed with some easier sections but in the course of a week or two you’d be sure to hit plenty of the hard stuff). Not to say the Whites are any easier, but there’s more support overall if you should need it.
_hoch_