Ours is in January as well... We have done the real "St. Johns on your own" back in 2010 and by that I mean that we went to Redhook to catch the ferry, but NCLs time in port is crazy early and short which makes this not a realistic possibility.... We are leading towards the excursion for no reason other than St. Thomas is like any other cruise port with the same shops...
Worse case scenario you can hang out in a much smaller, nicer town and best case for us we can hike the trail to the beach. It's About 1.2 miles away to Salmon Beach or 4.2 to Honeymoon Beach, with the trailhead being s about 10 min from downtown.
Lind Point Trail to Honeymoon Beach on AllTrails
https://www.alltrails.com/trail/us-virgin-islands/saint-john/lind-point-trail?p=-1&sh=gdgehp&u=i