Utah often has the best snow on the planet. To get this snow and the full Utah experience, Park City is not the best choice. The best snow is not at Park City but in two canyons about 45 minutes drive from Park City. In Little Cottonwood Canyon there`s Alta, which is the absolute best in terms of snow and fantastic terrain. But they are complete a$$**&(s who don`t allow snowboards. In the same canyon is Snowbird, which also has fantastic snow, but it`s not as varied in terrain. If you like steep and deep, though, it`s a great place. (Note that I haven`t boarded there since they opened their new Mineral Basin area--maybe that`s added some additional terrain--look into this). There`s just no comparison between these resorts and Park City. If it`s snowing the legendary Utah dry snow, get thee to Snowbird for at least a day.
There`s also a couple smaller hills in the next canyon over (Big Cottonwood Canyon), Brighton and Solitiude. Of these, Brighton has the better snow. Another chance to get the legendary Utah pow if it`s snowing. If you`re going for more than, say, four or five days, Brighton would be worth a visit.
Park City has the great nightlife (really the only nightlife), lots of restaurants and bars. The mountain is big and fun.
As far as the season length, I can`t answer fully but I have experienced huge powder dumps in the first half of April.
My advice would be to stay in Salt Lake City and rent a car. Ski the different places and decide which ones you like. Go to Park City for dinner and partying. Or, take the bus to the resorts if you don`t want to deal with a car. Alternatively. stay at Park City and rent a car. Get up 45 minutes earlier and drive over to Snowbird if there`s good snow. Note that the road to Snowbird can be closed if it`s snowing heavily until the avalanche danger has passed. Do further research into this before your trip so you can maximize your chance of getting great pow.
After you come back, please post a trip report and share your opinions of the place(s) you boarded.
Alta Rant: Alta is so damn nice that I rented skis just to go there two years ago. They are just such bastards about snowboarding. They`re mostly family folks (with just a few arrogant skiers mixed in), so it`s hard to get too mad at them. They sell enough season passes every year that they will never have to let boards in. Which is a shame because they just opened a mountain top connection to Snowbird, which does allow boards. I hope someone buys them and bans skis for five years just to give skiers a taste of rejection.