The USA is home to literally hundreds of fantastic ski resorts, and they are so widespread that you should be able to find a resort in or near most states.   There are a few things to consider when taking the children skiing.  Firstly, lift types and terrain varies greatly from one resort to another.  The ski resort's website should indicate the type of terrain it has and how much is suitable for beginners, intermediate or advanced skiers.  Secondly some fields might be ski - only, so if you have snowboarders in the family it's best to check!  Likewise, other ski fields may offer great terrain parks for snowboarding.  Accessibility is also an important factor - how far is accommodation from the lifts, and if transport is required, what kind and how family friendly?  Perhaps the most important factor is children's facilities. If a ski resort is family friendly this should be reflected in the programmes and facilities they offer.   Indoor childcare is usually available, but you will need to check the ages range accepted as some don't accept babies or toddlers.   Lots of resorts also have non-ski activities nearby, such as ice skating, ice climbing, heated swimming pools or adventure playgrounds.

Useful Reading
Leocha's Ski Snowboard America 2009: Top Winter Resorts in USA and Canada (Ski Snowboard America and Canada)

Top 15 Family Ski Resorts in the USA
- Steamboat Springs, Colorado
- Telluride, Colorado
- Jackson Hole, Wyoming
- The Canyons Resort, Utah
- Winter Park, Denver
- Bretton Woods, New Hampshire
- Deer Valley, Salt Lake City
- Smugglers Notch, Vermont
- Okemo, Vermont
- Sugarloaf, Maine
- Jiminy Peak, Massachusetts
- Northstar at Tahoe, California
- Yosemite, California
- Purity Springs, New Hampshire
- Whistler, British Columbia