A couple things, some of which have been sort of mentioned by PPs.
Define "American". Owned by a company based in the US? Or built in America by Americans? It's not the same.
Particularly cuz of NAFTA, a lot of cars built by the American based companies (Ford, GM, and Chrysler) are built in either Mexico or Canada.
Because of exchange rate, labor, shipping costs, and a variety of other things, a lot of "foreign" companies build cars in the US.
The list of what's what can get pretty exhaustive. If you could narrow it down as to what kind of vehicle you're looking for, that would help us tell you if a particular model is built in the US or not (and sometimes, some are built in the US while some are built elsewhere and you need to check the VIN to see if that particular vehicle was built in the US or not).
Finally, there's a lot of misconception about the Hyundai warranty. That 10yr/100,000mi warranty is just for the Powertrain. Meaning the engine and transmission basically. When people think of "warranty", they usually mean the bumper-to-bumper one. That one is 5 yrs/60,000 mi which is actually still quite fantastic. Even luxury cars only go up to 4 yrs/50,000 mi. But as to the Powertrain warranty, Hyundai isn't the best. GM will match it and Dodge actually beats it with a Lifetime warranty and Unlimited mileage. For the original owner of course.
Anyways, in the US, here's a list of the "American" based companies and their subdivisions:
Ford:
Ford, Lincoln, and Mercury. Also owns small stakes in Mazda (Japan) and Aston Martin (Britain). Used to own Jaguar (Britain), Land Rover (Britain) and Volvo (Sweden) but recently sold them. For the most part, those sold brands are still essentially "Ford" vehicles using Ford parts, engineering, etc.
GM:
Chevrolet, Buick, GMC, and Cadillac. Recently shut down Hummer, Pontiac, and Saturn, but they're still sort of around. All mentioned are "American" brands. Just sold Saab (Sweden).
Chrysler:
Chrysler, Dodge/RAM, and Jeep. Chrysler is the trickiest when it comes to being "American." Until somewhat recently, was owned by Daimler (better known as Mercedes Benz - Germany) and now is owned by Fiat (Italy). So, a lot of the current Chrysler/Dodges are essentially old Mercedes vehicles with a Chrysler styled body shell on top. Soon, they'll be Fiats with a new body shell on top.