Make sure you get away from Morzine would be my advice! There's tons out there apart from the main runs.
On the Pleney side, the green back down to Morzine isn't great, it has a lot of fireroad - but some really good bits too. Worth a crack for a warm up. The blue is ok, with some really nice bits in the woods but it ends halfway down so you need to either ride half a black or take the road part of the way. It's also slippy in the wet! The Pleney itself is red graded, and apart from a couple of bits isn't TOO much of a step up from red trail centre stuff. Far more roots and such though, just make sure you don't come barelling over a rise into one of the hard bits instead of taking the chicken run. Or alternatively, come over said rise and clear the tech bit in one go!
From the top of the Pleney lift you can head over to Les Gets (turn right from the top of the lift and follow the signs iirc) - the run down is actually really good fun, as are a lot of the linking runs. More natural, less steep. That'll bring you out to the bottom of the Chavannes DH / 4X track, which is great fun, but you do need to attack it a bit as the berms are MASSIVE. You can then jump on the Chavannes lift, which gives you LOTS of options.
You can take the main Chavannes DH, which is EASILY doable on a trailbike, and brilliant to session and get your confidence up on jumps and berms. It tends to be really busy though. So, take the green or blue run instead. These are both fun - the green especially in the dry, as it has some flat turns that get a bit slippy in the wet. They take you to a fireroad halfway down. Turn LEFT (away from the lift you came up on) and follow the road to another lift. From the top of this there are a selection of trails all of which are fun and all of which finish in the same place at the bottom of the lift. When you're bored of these, take the lift back up and turn left back to the top of the Chavannes. From here you can either head back down to Les Gets, or keep heading in the same direction back to Morzine - again, bits of this linking trail are great fun.
If you head back into Les Gets, head across town to the lift that Unk mentioned, and try the green. Again it only goes halfway, but if you follow the road from there you can pick up the black which is dead easy from that point. (It's trickier up top and fairly steep, especially in the wet). When you're done, head back to Morzine via the Chavannes.
On t'other side of Morzine, take the Super Morzine lift then the next one after it. I don't remember most of the trails from there, but if you head right you can pick up the track to Avoriaz / Lindarets. Iirc you head over a ridge then drop left on a fun bit of trail, pick up the road and follow it down into the bowl.
There are a selection of trails from the top of the lift on the Avoriaz side, all of which are more singletrack and natural feeling than a lot of the stuff around Les Gets. There are a few big features but they ALL have chicken runs, so take it steady the first time.
If you take the lift up the other side, you can drop down into Chatel for even more goodness. I would highly, highly recommend taking the green Panoramique route down - it's kind of like Spooky Wood on steroids, and is just ridiculously fun. Coming back down into the Lindarets bowl, I'd recommend taking the red / black DH rather than the fireroad - there's nothing really hard on it, it's just a bit steep. The fireroad is horrible! Then from the bowl you can just follow the road through the goat village back to Morzine, stopping off at Lac Montriond if you are so inclined.