Great for beginners, good snow, cheap prices.
Long transfer time......That's it.
Went on my first snowboarding trip January 2009, a squad of us decided on Livigno, i'm now totally hooked! Booked a weeks lessons with the Madness Snowboarding school, great bunch of guys, no more than 6 in our group, instructors very helpful, attentive and most importantly, encouraging and enthusiastic.
The resort itself is very cheap, both alchohol and cigarettes are dirt cheap if that's your thing. Eating out is also cheap, the food in Marco's is great but there are plenty of great restaurants dotted around the village. If you go at the right time of year, the Livigno Riverjump comp is on, part of the Snowboarding TTR tour, great night's fun.
The boarding/ski-ing itself is also great, once you get to grips with it as a beginner. A lot of more seasoned ski/boarders say that it is quite small and that you could do it all in a week, which is probably true but i've now been 3 times and i'm a firm believer that you make your own fun while you're there. There are plenty of wee runs where you can drop in of piste for a bit and there are now 2 bordercross parks at either side of the mountain as well as the excellent terrain parks, complete with airbags, for learning how to nail those landings of the big kicker!
All in all, once you get over the crippling transfer time from the airport, about 4 1/2 hours, you'll have a fantastic time.