Can anyone give me their thoughts on snowmobiling inside vs. outside the park at West Yellowstone? Also, if you go outside the park, are they any places to eat lunch?
Thanks,

Sure, West Yellowstone is in full swing during snowmobile season, it's the "snowmobile capital of the world." Not that there are a ton of places to eat anyway, as I recall. There's Bullwinkles and the Buffalo Bar for lunch. Running Bear Pancake House has a good breakfast, haven't tried their lunch. Madison Crossing Lounge is about the best, open for dinner but I don't know about lunch.

I take it you are aware of the restrictions for snowmobiling inside the park? If not: https://www.nps.gov/yell/planyourvisit/ncgsap.htm

Outside the park there are tons of places for snowmobiling. And the streets are not plowed - just smoothed, so you'll have both cars and snow vehicles on the road.

Are those restaurants in town? I thought I heard there is a restaurant on the trail that only snowmobiles can reach?

Those are all in town, yes. Once you get outside this rather small town proper, I really don't recall seeing buildings. How far outside town is it supposed to be?

I think the restaurant is somewhere on the Trail?