You may recall earlier this year, I divorced myself of Bank of America first by moving my banking to a local credit union and then, by cancelling my BoA Visa card. In researching credit cards, I went with the American Express Cash Everyday card. I have been pleased with the simple, yet good and fair rewards program and while they are also a big-ass institution, the research and reviews indicate some level of consistency and consumer fairness.
I have thus far, found 3 places that don't accept Amex:
(1) Sweetspot - this is a new fro-yo place that I happened to be near, and since they had a no sugar added option, I thought I would give them a try. I got my yogurt, it came out to $3 and some change, I had no cash at the moment and turned over my Amex to which the guy said, "sorry, we currently only take MC, Visa and Discover. It was a little embarrassing to tell the guy I had literally zero cash and apologized, handing him back my cup and he then said, "don't worry about it, thanks for stopping in (it was their first week open) and please, come back again. A few days later, I went in and brought the cash wanting to make good on my purchase and they were appreciative but insisted the first one was on them...been back a few times since. the guy did mention he was planning on accepting Amex soon...not sure if they do yet.
(2) Christmas Tree Shoppes - The thing that was odd about this is that they are owned by Bed, Bath and Beyond, who does accept Amex. I had waled around the store for a while and didn't have too many items but I had not enough in cash on me and wasn't willing to run to the ATM down the road so I just left my stuff on the register and left when they told me they don't accept Amex.
(3) Cost Cutters - I went to pay with my Amex after my haircut today and was shot down. I had enough cash but only with a shitty tip. I apologized but the nearest ATM, while not far, was not close enough to motivate me to go back - I'll make it up next time.
I thought about getting a Visa as well, for the times when Amex isn't accepted, but I hate credit cards and while I use them always, I do son only for the reward points, dollars - I pay off the bill in full every month, I haven't paid interest on a credit card in 21 years.