I live in a secularized country, where identifying as an Atheist is fairly common. I am curious regarding the "negative connotations" you mentioned. Which are they, and should I avoid revealing that I identify as Atheist when I travel to the US?
Realize I'm talking about a small minority, but they're also vocal. I doubt you will encounter them in tourist areas. In tourist areas people are more interested in your money then your religion, it just won't come up.
But in casual conversation with strangers, I personally identify as "Not Religious" instead of "Atheist". For some reason the term Atheist carries extra baggage in US.
For me, some American and a few European atheists appear to be as devout as the most strongly religious people I know. They are judgemental of others' beliefs, are absolutely convinced that their views are correct and disparage anyone who is even open or agnostic towards philosophical questions like whether there could be anything external to the Universe. These people dismiss any branch of rationality that is not directly measurable or quantifiable, and on one occasion I had to correct one by saying "yes, philosophy does actually serve a purpose, as a guide for which scientific questions we should tackle next".
That's a negative connotation I get when I meet someone who goes out of their way to let me know they're atheist. (This is a generalization which of course needs to be carefully balanced).
There are students who, having been excluded from school prayers at the behest of their atheist parents, are ostracized by the town.
There has never been an (openly) non-religious President. (And a single digit number of non-Protestant Presidents.)
A political candidate's piety, or lack thereof, is fair game for a political smear campaign.
Of course, reactions vary greatly depending on where you are. Coastal urban areas are generally much more atheist-friendly; an open atheist will, at worst, simply be looked down on by the pious. The inland "Bible belt", not so much. Atheism = devil worship, and exorcisms are a thing that are still performed.
(I've spent lots of time in Midwest areas that are well described as 'very Christian' and it simply isn't something that comes up. People certainly aren't talking about any exorcisms they have going on. I guess much of that time has accidentally been in areas with lots of Catholics and lots of not so evangelical protestants.)
If I'm not mistaken, that number is 1 (JFK).
(Also live in a country where having no religion is the norm and there are probably more negative connotations for identifying as religious.)