Snowbird would be my first choice for a boarder and skier, although it will be more crowded than Solitude, but probably not bad considering how sick the skiing will be. If there is a tram line there is still plenty of good skiing off the chairs. You can ski the Bird on a powder day without a tram pass and still hit everything.
They have had several feet of snow in the last week and are expected to get a few more from now through the weekend. If it snows they usually close the Little Cottonwood Canyon (Alta/Bird) early each morning for avi blasting and then open it at 8:00. If they have large slides this can change, with the next opening time usually being around 10:30, although nothing is certain and it can stay closed until the afternoon. If there is delay I would recommend not waiting and going to another area.
Big and Little Cottonwood Canyons often get a lot more snow than the back side of Canyons and Park City. I suggest checking the snow phone line that gives you all the areas to see who has the goods, then check the Alta phone for LCC closure specifics.
You have picked what looks to be an epic time for your first SLC visit. I will be driving their myself for skiing starting Friday behind the next big dump. If you go to the Alta website you can hit the link to weather forecasts and get the 24 hr LLC prediction.