I did a couple of weeks in Death Valley two years ago in January, and the weather was beautiful. That is an incredible place to spend lots of time, and winter is very bearable. We had a few clouds a couple of days (just enough to improve some landscapes), but otherwise cloudless. High temperatures in the low 70s F and lows at night about 50 F.
It is a huge place, so don't expect to do everything, unless you have a couple of months. Two weeks just scratched the surface.
I would guess that the South Rim of Grand Canyon and southern Arizona might be good in January, too, but I've only done that in March. Trips to New Mexico last year and southern Utah this year in April were very good, but on both trips a few key destinations were inaccessible because of snow.
That's my 2 cents.