Killington is an awesome mountain, it's personally my favorite mountain to ski on the east coast. It's massive (the beast of the east!) and has a lot of great restaurants and bars. They also have a good a mount of home rentals and hotels, but if you're looking for rentals near Killington, but not necessarily in the town - I'll share a few options.
We're a little biased here, as The Arched Chalet is in Plymouth, but it's a great spot for a few reasons.
In Plymouth there are a few rentals to consider, ours being one of them :). They don't have a hotel, but options via home rentals.
Similar to why I had Plymouth ranking high is that Bridgewater is also centrally located to a lot. Bridgewater is just about 10-15 minutes to Killington, and is very close to Woodstock and also a short(ish) drive to Ludlow (where Okemo is). That drive is around 25 minutes or so.
Bridgewater has a lot of great restaurants. Long Trail Brewery is just a fun go-to and Ramunto's pizza has excellent pizza, beer and is great for families.
Regarding lodging, there is the The Bridgewwater Inn, we haven't stayed there, but it's a consideration. Further, there are rentals in the area.
Rutland is about 20 minutes from Killington. While we haven't personally stayed in Rutland, I'm including this as it's a small city. If you're looking to stay in an area with the standard shops, grocery stores, movie theaters, etc. this would be a consideration. They also have an airport (you can fly direct from Boston to Rutland).
However, Rutland isn't as rural, so if you're looking to get out in nature - I would suggest other towns, but had to include it due to close proximity.
In terms of lodging, since Rutland is more of a city, there are standard hotels and you could also find home rentals.