Looking for luxury in Park City

If you want full on luxury experience and money is not an object (which i assume it isn't since you specifically stated you wanted luxury)I would stay slope side in deer Valley. There's the Stein Ericsson Lodge, Montage, and St. Regis. I have been in all three. (As in walked in and looked around, I don't believe they would actually let me stay there) . All awesome looking digs and slopeside. I suspect they all have shuttles to Old Town if you want to go there for shopping or restaurants. Also, take a look at Park City Visitors bureau..  

The word luxury can mean different things. So with that in mind, if you are a Four Seasons, Ritz Carlton kind of family, then its likely you will like the St Regis at DeerCrest in DV or the new Montage on the Empire side of DV, or perhaps the Stein Erikson lodge in Silver Lake DV. Park City also has a few luxury hotels but none I think are ski-in/ski-out, and in the Canyons, the Grand Summit is Ski-in/Ski out. And in DV, PC and the Canyons there are some rather extreme-lux condos available too, look on the web on the respective resort sites. 

If you like smaller inns, and that sort of feel, then in DV the Goldener Hirsch has the Euro feel, and Alta has the Rustler Lodge (we stay in Alta Lodge when there)

Where did you end up?  I've lived in PC for 7 years.  Agree with the DV recommendations.  Canyons has just as luxurious Waldorf Astoria, but it's not literally right on the slope, and I wouldn't go to the Canyons anyway with younger kids.  Had too many close calls with  my five year old up there last year.