I've been skiing and snowboarding for many years and have, in fact, taught both professionally. I love Vail, but Copper wins my vote as the best all around resort in Colorado. Here's why... Copper is designed with a family in mind - the mountain is roughly divided by terrain so that beginners will not get caught on something too difficult, and vice-versa for experts. Copper has a great learning center away from the main mountain putting both beginners and everyone else at ease. The snow is great and so are the runs. Great new bowls also make the experience great for experts. Finally, the trip from Denver is just over 1.5 hours so it's very convenient for day skiing.
Pros: great design, beginner friendly, not too crowded