I would certainly try to attend at least one game if I were in NYC. It's not Fischer-Spassky, but the world championship is still a pretty big deal, and as you noted, it's a nice bucket-list experience -- at least, for those of us who care about the game and its history.
Carlsen is the clear favorite. Although he had an uncharacteristically bad stretch for a few months last year, he reasserted his top-dog status toward the end of 2015, and he's continued to play solid chess in 2016. Yesterday, he took a break from his match preparation to defeat Nakamura rather comfortably in the finals of the Grandmaster Blitz Battle Championship, which brought together most of the top blitz and bullet chess players in the world.
Karjakin comes into this match with a much more uneven record over the past couple of years. Last year, he was the surprise winner of the World Cup, an unusual single-elimination tournament combining classical, rapid, and blitz play, and that victory qualified him for this year's Candidates Tournament, where he again emerged as the winner. Despite these successes, however, his classical rating is currently only ninth in the world, about eighty Elo points below Carlsen. There has been speculation that his fairly mediocre results over the last two years reflect a change in priorities -- he was married in 2014 and became a father last year -- but he still has the raw talent and skills to pull off an upset over Carlsen. His best path to victory is probably to win an early game and then hang on with a bunch of draws. Karjakin is not a very flashy player, but he is one of the toughest players in the world to beat.
I'm not aware of any bad blood between Carlsen and Karjakin, who seems like a pretty mellow guy.