Butternut is our family's go-to for many years. It's definitely not a 'modern' resort, so if you expect condos and lots of shops/bars, you need to go further north. But it's 1000 feet with a fun mix of trails and a perfect day trip from CT. It's farily easy to avoid the crowds if you stay off the quad lifts. On the weekends, there's a triple chair that gives you access to fun blues once the crowds arrive at 10 a.m. or so. By 2 p.m. the slopes on the main lifts open up again and from 3-4, you'll cover lots of territory.
Ski instruction is some of the best in southern New England and the lift operators on PaddyWagon will actually help young ones learn how to properly ride a lift. Once you head to the top of the mountain, there isn't a lot for the beginner. That's one gap of the mountain, but after a few days slowly cruising the blues, kids become comfortable.
As was mentioned by others, the main area to eat is up on the hill and a bit of a walk without any steps to help. If you bring food to eat, you probably want to drop someone off at the top parking lot to walk it over rather than walking all the way from the main ski area.
So - 1) weekdays are awesome! 2) Get there when it opens and ski the main trails until 10:30 or so. 3) Head over to the triple and take a few runs. 4) Get into the lodge before Noon and be back out at 12:30 when all the families eat. 5) Back to the triple for an hour and then ski enjoy the whole mountain for the rest of the day. 6) Look at you SkiTracks app and realize that it was the best $dollar/vt ft you're likely to get without driving for 3+ hrs or flying.