I will be leaving in the evening. What would be the best way to go? Is it doable in two days/two nights to go there and back?
My S and I drove from Lexington to Princeton after Christmas break. It is a long day of driving (about 10 hours). And that was without snow (although we did have rain most of the way). We took I64/I79 through West Virginia to the Pennsylvania Turnpike. I think that’s the shortest route. I will not tell you if it’s “doable” but it will be 10 hrs each way!
We drive straight through all the time. The drive is 10 hours, depending on what time you roll through cities or encounter weather in the mountains. Leaving at night will save having to worry about rush hours. We usually go the PA turnpike to 70.
Yeah, I guess if your driving at night, you won’t care about the pretty scenery through WV 
I will probably stop around 11pm the first day. Could you suggest a good place to stay overnight on the way?
Somerset or New Stanton, PA will let the weather decide if you want the scenic WV and Eastern KY route in the morning. The bonus is there is a lot less traffic on 64. Nothing like Charleston, WV to clear the sinus.
The traffic between Charleston and Huntington WV can sometimes be crowded. A good route is the Penn turnpike to I-68 through Maryland, then I-79 to I-64 in Charleston. The scenery through WV is gorgeous (I grew up in W.Va.). There are good places to stay in Charleston and in Huntington and also around Clarksburg and Fairmont WV. In MD, Cumberland has several places to stay. And yeah - hold your nose around Charleston! pee-uuuuu!