Evan ProdromouLet's say that NATO wanted to do a preëmptive attack to seize some US territory in anticipation of an invasion of Greenland. (Holding a territorial bargaining chip is a great way to get your territory back at the end of the conflict. Also, the US public is not used to having the homeland occupied, and would not be willing to live with a loss of territory for very long.)
Evan ProdromouI think the best candidate for taking a chunk of territory would be somewhere along the Alaska-Canada border. But that really requires some aggressive action by Canada, which has a lot to lose in starting that kind of war.
Evan ProdromouAnother option would be seizing unoccupied territory along the border between the lower 48 and Canada. There's a lot of sparsely-populated land up there, and it'd be possible to get a big, scary chunk of the map coloured maple-leaf red on the nightly news. The parts of Maine north of the 45th parallel are very empty and would actually be quite nice to have on our side, anyway. It's a pain to have to drive around them to get to New Brunswick!
Evan ProdromouMost US overseas territories aren't great candidates. The US has a lot of territories spread across the Pacific, which are hard for European powers to take and hold.
Evan ProdromouI think the Caribbean might be good. The US has a huge, neglected territory in Puerto Rico, with historic ties to a European power (Spain). It would be interesting to start negotiations on defence arrangements with an independent PR, or some hoohaw of that sort.
Another option is the US Virgin Islands -- formerly a Danish colony, so some good optics there.
Evan ProdromouOne that might be fun is Navassa Island, the last of the US's guano island holdings from the 1800s. It's a little uninhabited dot between Jamaica, Cuba, and Haiti. Most Americans don't even know it exists. The claim is kind of shaky, too.
https://en.wikipedia.org/wiki/Navassa_Island