We love Park City! Our favorite place to stay is Marriott Mountainside. Its ski-in/ski-out and very family friendly. You don't mention specifics - when are you going and how many people? You will find most places are condos not really hotels. The Marriott is a vacation condo place, so your cheapest option is to rent from someone on Ebay or VRBO, rather than go thru Marriott. We have also stayed at the Lodge at Mountain Valley, also ski-in at Park City resort. The units there are individually owned, so some may be nicer than others.
If you have any specific questions, just ask!