My experience was not in the USA, but in Canada. Been there 2x. First time I did currency exchange, company credit card, and personal credit card. Besides the hit you take on cash exchanges, any money not spent is another loss if you exchange back to US currency. In Canada, they will take American money on a 1 to 1 basis because they keep a extra 35% or so from the exchange rate. But of course not the other way.
On credit cards....Visa and MasterCard are a go. Discover is hit and miss. Stores like Wal-Mart and target, along with the large chain stores accept them, but smaller mom and pops, not so much. I went to a Burger King, and the clerk had not even heard of discover card. Another benefit to a CC, is that the card company will automatically apply the currency rate to your purchase. So a dollar spent might only show for example a 65 cent charge. Never never use a debit card on the road. Use the built in protections a CC will give.
Travelers checks, good luck. They are a thing of the past. My mom spent 2 hrs plus....At her bank,....redeeming some older ones she found. They knew her as a customer for years.
On my 2nd trip, just used a CC, for almost all my purchases, and on another note, paid a extra $10 on my cell phone for a month, to get international calling. A very cheap alternative to phone cards or ala-carte phone minutes.
As others have said, having both just makes sense. It covers all aspects of a trip for unforseen emergencys.