Avoriaz has a "Snow Cross" run, Brocheaux, accessed from either the Prolays or Brocheaux lifts. Snow Cross is a controlled, off-piste run. Basically, it's good, un-groomed terrain, that's only open when it's safe to be open. You can get some good fresh lines here, but being close to the mainstream area, you need to be quick. Also close to hand is the Pointe de Mossette - if you have the full area pass.
If you're looking for something not too advanced with no walk out issues, Pré la Joux has a few things to offer. From the top of the Chaux des Rosées lift, drop off the blue just after you pass the black and start traversing skiers right. It's fairly short, but you'll find yourself in a quiet, wide chute. Good enough for some nice turns, it runs out onto the black and you can spot most of it from the lift up. You can drop off the black again for some more pow before returning to the lift.
From the top of Des Rochassons, duck under a rope on skiers left to access a face leading back down to Les Lindarets. Make sure you know what you're doing.
The black runs in Pré la Joux are steep, if that's your thing.
Once you're on the hill, starting from Lindarets, you're looking at a combination of the Avoriaz area and the Pre la Joux/Linga area. For freestyle, this is good news. Closest to hand is the Stash. Sponsored by Burton, Avoriaz puts a lot of effort into this 'natural' freestyle area. Each year they look at new ways of adding interesting features, which unlike in the beginning, are now suitable for all levels. It's more 'jib' oriented, so you won't find huge kickers here, but that's not what the design is all about. Rather, the park builders look to provide natural lines that flow through the Stash. And they succeed. Rails and boxes built from logs, pic-nic benches, wall rides, hips and rainbows. It's all there.
More from Avoriaz, there's the Chapelle park, one lift away, great for beginners through to strong intermediates. This park has a strong scene, and you'll find plenty of people here who know what they're doing. Park upkeep is excellent. You also have the halfpipe, which can be found in the centre of Avoriaz, close to the top of the Prodains cable car. It's well shaped.
Linga offers the Happy Park. It's designed for advanced freestylers, huge kickers and all that. It might not be built as early in the season as the parks that Avoriaz puts out.
Montriond has no immediate slopes of its own; when considering this small resort, the 'local' terrain on offer is actually considered to be a combination of the Avoriaz slopes and the Pre La Joux/Linga slopes. This is the Montriond-Avoriaz pass, based around the Lindarets area, and if you don't want the full area pass, it represents a good selection from the huge Portes Du Soleil. You'll find the exact piste map on the tourist office's website; this pass covers the majority of Avoriaz's slopes with the addition of Pre La Joux and Linga.
Les Lindarets can be accessed directly from Ardent via the cable car, which in turn is only 5 minutes from Montriond using the free bus service. As a base, Les Lindarets is pretty central in terms of the whole area, making it great for Portes Du Soleil access. It also acts as a hub, providing a number of restaurants for eating on the hill. However, this configuration also means that the slopes leading down to the base can get quite congested.
There are some good blues running off of the Prolays lift. Long enough to get a good sense of opening it up, with good variation in pitch too. Pré la Joux offers some great terrain for those who like challenging pistes. The reds running off the Rochassons and Plaine-Dranse chairs are fairly long with fast, steep sections; be aware that they're likely to be mogul'ly in the afternoons. The black, Les Renards is tough for sure, but it's probably more appealing to skiers, unless there's been a fresh dump.
Le Linga is another good red; running from the top of Tete du Linga all the way to Linga's base, it's as long as you'd like with a nice mixture of gradients. Carve away.
If you are shredding in the Pre La Joux valley be sure to keep an eye on the time. The crucial lifts are Pierre Longue and Plaine-Dranse. If you get stuck in this valley after the lifts close, it's neither a simple, short or cheap journey home.
Stepping off the Ardent cable car, there's nothing in sight that's ideal for the absolute beginner. However, both the Prolays and Lindarets lifts give you access to Avoriaz's beginner area, serviced by two button lifts, Ecoles. It's a great place to start. If you want lessons it's worth considering the Mint Snowboard School. A group of British snowboard instructors who continue to receive good feedback, might provide a refreshing change from the usual ESF, and you'll have no problems spotting them
This area of Avoriaz provides some good blues for practicing those linked turns. Procluo is popular, even if there is a slight flat section. If you're feeling more confident, the blues running back to Les Lindarets will take you to the next level.