Part One: What specific forests (county, state) do papers like the NY
times Newspaper or the San Diego Union Tribune Newspaper get paper
from? Part Two: Is there a list of major newspapers in the US and
which companies they buy thier paper from, and where these companies
harvest the trees that make the pulp that go into the paper?

I don't have the specific information you're looking for. If it's
helpful, I do know that most paper is made from wood that is
considered useless as timber. A major source of such wood is southern
tree farms. Trees are initially planted close together to limit light.
This produces the long, straight, unbranched logs required for timber
products. When the trees reach a certain size(6 inch trunks for
instance) they are thinned to allow the remaining trees to grow
faster. The thinned trees are a waste product that pulp plants can buy
at very low prices. In this case the pulp doesn't come from natural
forests as such. The tree farms provide a more renewable wood source,
producing a crop of saw logs in as little as twenty years.