Here's where you see the snow and condition report: http://prance.com/whitefaceGroomMap.asp
(someone else on here pointed this out).
The Hungry Trout
Motor Inn and Restaurant is about as close as you can get to the mountain, one mile away from the parking lot. Well, on second thought there are some cabins and a smaler motel slightly closer, but I don't know their names.
If you stay in Lake Placid, it's no more than 15-20 minute drive. The tradeoff is that in LP, there are cool bars and restaurants, whereas nearer the mountain, (officially Wilmington, NY), there are only two or three bars and same # restaurants, and maybe one convenience store that does not stay open all night. Ask yourself if you're going just to ski, or to ski and also soak up some nightlife?