Being an Italian Catholic likely to be living in NYC, it would have been Kennedy hands down. Nixon I would not have cared for at all, ever since the late 40s and early 50s. I would have liked Eisenhower, though, but not tied my like of Eisenhower with Nixon, who was a different kind of Republican entirely.
That said, I would have secretly known that the Kennedys were corrupt and that the Kennedy father was an anti-Semite and not cool in my book, because I would have been a liberal (likely by 1960 a Democrat although possibly a liberal Republican from the Northeast) and I would have strongly opposed and challenged anti-Semitic attitudes that were very prevalent (and still are) in the United States.
Had I been born when my grandmother was, I would have been 25 in 1960, old enough to vote by 4 years. I would have also been a homosexual - possibly an avowed (as was the parlance at the time) homosexual - but like all the others for the most part I'd be hidden. Only in the 1960s and 1970s (into my 30s and 40s) would I have begun to venture out into the world and read gay literature or go to a gay political meeting.
I don't like bars so I most likely would have not been at Stonewall that night, but I would have known about it maybe through some other men that I knew and would have 100% supported the new movement that was springing up from it - even if I was closeted.
So it would have been Kennedy. Johnson would have scared me, ironically (since 21st century me thinks very highly of him in many ways, none of them of course associated with the lies that the government began telling the American people about the war in Southeast Asia).
Kennedy possessed youth, charisma, and really a new kind of politician. Not only could he so get it (and I'm sure for closeted gay men that was understood right away just by watching him talk), but JFK was actually ing inspiring as sh**t. He really was quite benign, even though he did cheat on Jackie left and right, but he seemed like a really nice, cool guy. Rich preppy yes, possibly privately elitist, but JFK exuded real appeal. He was a guy you'd want to have a beer with. Whereas Nixon was kind of the dude that would have a few drinks and then get thrown out of the bar for pissing off the bartender.
lol anti-semitism is not at all prevalent in the US.