Don't know that I've ever seen/found any 'well-filled' American beechnuts,
though most of the trees I've had occasion to check have been isolated
specimens in residential yards in town. There are a few in my woods - and
more on the hillside across the creek, but I've never actively gone out in
search of the nuts. Just doesn't look to me as though there's be much
there to eat.
Had a friend from NY send me some American & European beech nuts a couple
of years ago - the Europeans are much larger & meatier. Didn't eat 'em,
planted 'em.
Took a drive through Bernheim Forest Arboretum last week, on my way back
from the State Fair(my local shagbark hickory selection took first place!),
but I didn't get out and walk through the 'Beech Grove' area - they have a
number of the European beech selections - purple, copper, weeping,
tricolor, twisted, etc. Anyway, collecting is prohibited there, but I know
a couple of the guys there, and they would probably allow it, if I asked.