My wife is still progressing but being a beginner, scratching on the surface of intermediacy, she finds a few runs she likes and is content lapping those all day.
That's good info to know. I'd be cautious about Snowbasin or Snowbird for the family in this case... they have very little terrain that would be labelled "green" at most resorts, and not many easy intermediate runs either. On the other hand, both mountains are phenomenal for advanced intermediate and beyond.
I think a family Alta/Bird pass would be within a few hundred of Powmow/Snowbasin so that's an option if that gives enough terrain for our only pass.
Looks like the wayback machine doesn't have AltaBird pricing from this past fall, but for 2016-2017 the family pass was $2799 (https://web.archive.org/web/20160906005552/https://www.alta.com/visit/tickets/ticket-info-pricing).
I agree that Big or Little Cottonwood could be a fantastic choice if you can afford to live up in the canyons. I think there's pretty broad consensus that Alta is the #1 spot in the country for snow. Snowbird, Brighton, Solitude, & PowMow all report 500 inches average snowfall... seems like maybe a little exaggeration with PowMow and Solitude, but not so far off as to be unbelievable. But generally you're talking about gradations of A+ here (at least when compared to the country as a whole), and all of these mountains get and keep significantly more snow than just about anywhere else in the country (Wolf Creek, Grand Targhee, and maybe Mt. Baker are the other tops).