Cooper seems somewhat more American than most companies in what has become a highly globalized business. They have a reputation as a decent place to work. However, they also make tires in, or have cooperative deals or ownership stakes in, factories in several other countries. Those tires may or may not be destined for the US market (and tires made here may or may not be destined for export).
This is true of a lot of tire companies, whether at top level they appear to be foreign or domestic. The details of which tires are made where for whom tend to vary quite a bit in response to a lot of factors, including (in no particular order) labor cost, raw materials prices, logistics cost, currency exchange rates, trade negotiations, and the ebb and flow of demand in different markets, as well as which factories are set up to make what kinds of tires.
So if you want to support business in the US and/or your home state, Cooper would seem to give you a better chance than most -- but you have to check the country of origin of your particular size, model, and brand of tires -- maybe even of your particular tires! I think it's required to be marked on the sidewall and certainly is required to be available to the consumer through some means.
If you're worried about quality... well, I would trust name-brand tires made in most of the advanced, industrialized, and relatively free nations, and would be suspicious of tires that are remarkably less expensive than their competitors. Tester and consumer ratings that you can find on tire-related websites can also tell you something useful.
But when it comes down to the actual country of origin, only your sidewall knows for sure...
--Joe