I am wondering if American currency is accepted in South Korea?

No.

Yes, most currency exchanges will be happy to take your dollars in exchange for some Korean Won.

And, of course, currency exchanges will be more expensive than many other ways of getting South Korean Won.

I assumed the OP meant hotels, restaurants, shops, transit options, etc.

I can also report that U.S. dollars are largely accepted in large establishments, especially in the major cities. In smaller shops it's more hit or miss but some do. It's easiest to have at least some won handy.

I did too, Kia. Guess I should have added a smiley face...

I am actually Canadian not American, but have found that US$ are more widely accepted in my travels this far. On our cruise we're having a DIY day at Jeju Island & wondered if we could get by without purchasing some won from the currency exchange here.

Not all places will accept U.S. dollars, but many will although you'll get change in won. The larger establishments accept credit cards too.

Cruise ports often have booths/shops specifically aimed at clueless and/or corralled cruise passengers, with high prices (even after you have bargained) and lousy exchange rates. But if you're only there for a few hours maybe it doesn't matter.

The best way to get local currency almost everywhere is at an ATM, from a bank account that doesn't charge foreign conversion fees. There are numerous threads on this site (especially on the Europe board) about that.

You can buy even an ice bar (less than a dollar) with a credit card in South Korea.

There are a lot of interesting things to see in Jeju, but none of them are anywhere near the cruise port (which is on the north side; most of the interesting places are on the south), so you'll need Won for the bus or taxi if you are DIY.

I suspect that whitecloudorillia has already returned home, but just in case anyone else consults this thread:

"There are a lot of interesting things to see in Jeju, but none of them are anywhere near the cruise port"

Actually, Jeju Mokgwana (a former Jeju government office complex) and the Gwandeokjeong Pavillion (the oldest wooden building in Jeju, just outside the main gate to Mokgwana) are both in Jeju City, not far from the port.

yes US dollars are the easiest to exchange in korea but Don’t forget to reconvert any surplus won into another currency before you leave the country, as exchanging won outside Korea can be difficult.