Keystone has a great little hill to teach young kids to ski. The area has the two longest "Magic Carpets" i have ever seen and you can use them even if you are not in the ski school. Most other resorts limt access to the Magic Carpets to kids in the ski school which usually runs for $125 plus lift ticket. Next to the the Magic Carpets is a short two person lift that supports a small hill. We took our 5 and 6 year old on this hill and after two half days they were ready for a regular green hill.
On the downside, most of the green hills are trails with quite a bit of flat area.
My wife and I skied the River Run which has some really nice Blues. We were also surprise how short the lift lines were during New Years week. One tip, if the new River Run Gondola has a long line, try the River Run Quad chair. It goes to the same place, is just as fast, and usually has a much shorter line.
We also did the tube run. It is a lot more extreme than it looks on the internet and is probably a little too wild for kids under 8 or 10. Plus it is at the top of one of the peaks at about 11,600. One of my kids got a bad headache from the altitude and it ruined our time on the tubes.