Mercury. is visible in the pre-dawn (eastern) sky during much of January. Maximum elongation occurs on Jan 17.
Venus will high in the sky throughout January. Maximum elongation occurs on January 12, but the planet will not noticeably decend (back toward the Sun) until around mid-February. Venus and Mars appear to move toward each other during much of the month. They get to within 5.4° by month's end, but then begin to slowly move apart from each other.
Mars is fairly high in the western sky throughout January. See note on pairing with Venus, above.
Jupiter (in Virgo) is bright in the eastern sky a few hours before dawn. By month's end, the gas giant will rise a little before midnight.
Saturn begins January lost in the Sun's glow. By late in the month, the ringed planet is visible in the east about an hour before sunrise.
Outer Planets. Uranus and Neptune. Neptune (in Aquarius) begins the month is in the western sky near Mars at dusk. It passes very near Venus on Jan 12. By month's end, it is very low in the western sky at dusk. Uranus (in Pisces) is a couple of hours higher. It's nearly overhead at dusk in early January, and still high in the western sky at month's end.
Pluto is lost in the Sun's glare during January.
Comets, Asteroids and Meteor Showers:
Comet 45P/Honda-Mrkos-Pajdusakova - is in the evening sky during much of January. It spends most of the month in Aquarius, and is visible thru binoculars or a modest telescope. It's a fairly bright comet, and may approach magnitude 6 during the month.
Comet C/2016 U1 ( NEOWISE ) - is another bright (magnitude 6-ish) comet that is gracing our skies. It will be visible in early January in the pre-dawn eastern sky. By mid-January, the comet is lost in the Sun's glare, and will not be visible again in the Northern Hemisphere.
Constellations and Deep Space Objects:
January features the winter Milky Way. Auriga is nearly overhead at 8 pm with Orion and Gemini fairly high in the east (map shown at right - click for a larger image). No fewer than nine bright Messier objects are visible in this fairly small region of the sky. The brightest is the Orion Nebula which is visible to the naked eye. Binoculars or a modest telescope reveal the cloud-like nebulosity. A larger telescope brings in a stunning view of the expansive nebula (shown below, left).
Auriga appears as a pentagon or hexagon in the sky depending on how many stars you include. The constellation is famous for its open clusters. Several bright open clusters are visible using binoculars or a modest telescope. Three of them are visible simultaneously thru binoculars.
Gemini is most famous for it's two bright stars, Castor and Pollux. Both are multiple star systems, but Castor's brightest pair of stars can be split pretty easily using binoculars or a modest telescope. Castor A & B orbit each other with a period of 445 years. Sometimes, the pair are so close to each other that a larger telescope is requried to split the pair. The current separation is about 5 arc-seconds, so should be pretty easy so see.