Which could be the best option for a three-week holiday in the USA? Just need to make and receive a dozen phone calls (only simple phone calls!)

Generally, a T-Mobile prepaid or one of the MVNOs that run on T-Mobile. The exception would be if you plan to be visiting remote places like backpacking in national parks or something like that. T-Mobile often has coverage issues in remote areas (like Wind).

As DrNewcomb said, Tmobile or even AT&T should be fine for just calls. Actually, I think AT&T is $0.10/min and tmobile is more than that. Just visit their respective websites to see your options.

Close but no cigar
 

So my wife went into a NYC AT&T store and bought the SIM card kit. They apparently tried and tried to make it work with the HTC ONEXL but couldn't (not sure if they couldn't turn off LTE or what?) so luckily she had an old (3) iPhone with her so they put the SIM in that and she had to use that as her connected phone.

Pretty poor of them - it may help for others if someone could suggest what they might have done wrong - I would have assumed AT&T would know what they are doing :/

have a look at piranha mobile simcards...

In the US, the HTC One XL should work on GSM 850 & 1900 and 3G 1900. Unless there is some setting that restricts the HTC to certain bands, it should have worked on at least one of those bands. Don't know about the LTE.

It should have worked. A family member visited from the UK with that same phone, it worked with an AT&T prepaid sim without problems.