When are you travelling?
The area around Lenzerheide is great. You are spoiled for choice in the region even though the main lift in the resort itself is closed this year.
It is possible to ride quite easily between the resort of Davos, Arosa and Lenzerheide on some great single trail. There are quite a few routes from Lenzerheide itself depending on whether you want to ride up or use the lift.
Lenzerheide is 20mins by car from the new Alpen Bike Park in Chur which has 5 lift assisted runs (Haven't ridden them yet though). Its possible to ride down from Lenzerheide to Chur on a mixture of trail and fire road and then possible to ride from the top of the lift in Chur predominitaly down hill on some good singletrail with a bit of fire road thrown in too.
Lenzerheide is 40mins from Flims/Laax which has a couple of long freeride trails and also some really nice natural trail riding in the area.
Lenzerheide is just over 1 hour from Engadin which has more trail riding then you can shake a stick at.
You could Ride from Lenzerheide to Tiefencastle (on trail) then get the trail from Tiefencastle to Davos, Ride tons of singletrail in Davos and then ride single trail almost the whole way back to Lenzerheide at the end of the day.
In the Canton Graubunden (where Lenzerheide is) MTB is allowed on nearly all of the hiking routes. Its much more bike friendly then the area around Grindlewald appears to be. If you need some tips for the area let me know. If I'm around when you are here I might come up and show you some stuff.