The New Horizons probe will zip past the small Kuiper Belt object “Ultima Thule” at abut 12:30 AM eastern time (10:30 PM Mountain). NASA TV should cover it, but there’s also Ye Olde Interwebs:

How to Watch New Horizons’ Ultima Thule Flyby on New Year’s Day: A Webcast Guide

Given the distance and the consequent low data rate, I don’t imagine images will be forthcoming. Those will probably trickle in over the subsequent days, assuming the probe survives. Even now Ultima Thule appears as just a single pixel, but the light curve has been sufficiently puzzling that one explanation has been that it is surrounded by a cloud of particles or micro-moons. Which would be awesome, so long as New Horizons doesn’t hit one of them.