Park City w/Kids

Taking the family to Park City for a bit of skiing next week. Staying at Hotel Park City, near intersection of Park Ave and Kearns (looks to be about 2mi from Main Street).

Looking for recommendations for dining spots (dinners mostly) that are suitable for children (5 and 7). Bonus points for BYOB as I’ll likely be bringing a few bottles along for the trip.

Also, curious about other non-ski activities. We’ve looked into snowmobile rides and dog sledding - anyone done either in/near Park City? The former sounds like more fun, but unsure if it’s a good idea with kids. Would also love to go sledding (downhill, not dog) one day. Gorgoza Park was the highly rated sledding park on the interwebs but appears to be closed this season. Any other spots to check out?