This year may have been a grim one on many fronts, but the heavens are at least giving it a good send off. Wherever the skies are clear, there will be two comets visible via binoculars on the night when 2016 turns into 2017.
As the Sun sets on December 31, Venus will be bright in the western sky, accompanied by a much fainter Mars. If you make a line from Mars to Venus and then keep going about the same distance, you will find yourself not far from Comet 45P/Honda-Mrkos-Pajdušáková. Unless your eyesight is excellent and you are well away from interfering lights, you won't be able to see it unaided, but binoculars or a small telescope should show at least the comet's head and possibly even the tail. Depending on your time zone, the comet may be quite close to the crescent Moon, which will be faintly visible at the time.
If you do some serious partying and are still up shortly before dawn, you may get a chance to see a second comet, named C/2016 U1 NEOWISE. It's currently in Ophiuchus, the zodiac constellation astrologers prefer to forget. At this point, C/2016 U1 NEOWISE will be too faint for the naked eye, even under the best conditions, but binoculars may bring it out. Moreover, it should get brighter over the first few weeks of the new year.
It's not unusual for there to be two or more comets in the sky at once, but the overwhelming majority are far too faint to see without telescopes. Two that are either at the edge of visibility, or are expected to get there soon, is an unusual conjunction.
Moreover, the two comets represent a stark contrast. Comet 45P/Honda-Mrkos-Pajdušáková is a short-period comet first discovered in 1948. With an orbit lasting just 5.25 years, it has been back 13 times since. Sometimes, however, the Earth has been on the wrong side of the Sun for a good view. This time, however, we should get a better look. It's visible in Capricorn, so Southern Hemisphere observers will get the best view. It's getting closer to the Sun, so it will become harder to spot if you miss it tonight.
On the other hand, C/2016 U1 NEOWISE has an orbit of at least a million years, and indeed may never have visited the inner Solar System before. This makes it far more unpredictable in its brightness than 45P/Honda-Mrkos-Pajdušáková. Depending on its mix of dust and volatile compounds that will turn to gas with the Sun's heat, it could become quite bright or be another on the list of comets that never lived up to expectations.