I stayed in Flims over Chrismas and New Year 2006/07 with my wife and 4 year old daughter. The snow wasn't fantasic and at least 50% of runs were closed. However, we all had a fantastic time.
The ski school was fantastic with our daughter and still managed to find suitable runs to keep her occupied on her first ski trip. Whilst there was little or no off piste availble, the resort managed the pistes well and used the snow canons whenever the temperature dropped sufficiently.
In addition to skiing, the resort was well-geared up to other activities. There is a fab indoor skating rink, sleigh rides and all the other attractions that you would expect from a top class resort.
We stayed in the Park Hotel Waldhaus and would highly recommend it. In fact, we're quite likely to stay there again and we're not usually into going back to the same place twice.