Just one person's opinion...
Many experienced US skiers will tell you the single best place for powder is Alta, Utah, but there are a number of other fine choices in Utah, Colorado and elsewhere in the US. Frenzied powder hounds have been known to descend on Alta on storm days, so it might not be the best for crowd avoidance on days when there is significant new snow. Some Euros find that flights are significantly cheaper/better into Denver than Salt Lake City. Those two cities are usually the most affordable gateways to powdery ski slopes in the US. If you go to Utah the cheaper way to experience the great skiing is to stay in an inexpensive suburban Salt Lake City motel (such as the Crystal Inn) about 30 minutes from some of the best ski areas. Rent a car and commute each day to the resorts using something like the Utah SuperPass for Alta, Snowbird, Brighton, Solitude. There are other good choices in UT such as Snowbasin and Powder Mtn, and Park City.
If you go to Colorado there are many choices known for good and relatively comparable snow conditions such as Copper Mountain, Winter Park, Steamboat, Vail, Breckenridge, Aspen, etc. You must research them to see which may best fit your budget and plans.
In my humble opinion the period from late February to early March provides the best combination of good snow conditions, yet a fair amount of pleasant sunshine in the Rocky Mountains. You can search this site for more details on many things mentioned above. Here's a recent thread that might be informative: http://www.epicski.com/forum/thread/101611/best-bet-for-starter-powder