I have many hickory trees dropping their nuts between September and into November around the yard, so I can pick hickory nuts to eat, but since I am competing with the squirrels, I do not bother picking them. Other nuts I forage during this time of year are Walnuts and Pecans. I find that Walnut trees have become prevalent on the sides of roads in Kentucky, so you'll most likely be able to harvest a bucket full of walnuts when walking along roadsides. Every year, James and I pick walnuts and pecans.
Fruits to forage this time of year are Pears, apples, and persimmons. These fruit trees may not be growing in the woods, but they may be growing in an abandoned lot or alongside the road; but there is no need to forage these fruits when your neighbors have them growing in their yard. I have actually picked some apples and persimmons from neighbors' trees because they did not want them.
My struggle with picking persimmons is that I have to wait till they drop to ensure they are ripe. I recommend freezing persimmons overnight to take out the astringent properties. Here are the photos I took of our Apple and persimmon forage. I did not pick many persimmons because there were not many on the ground. It seems that the squirrels and other critters are getting to them quicker than I.