When I've been on the west side, I headed to Puerto de Santiago, then Santiago Del Teide where there's some nice switchbacks. From there you could either explore further North, where it gets a bit more green, or head South East towards Chio and see if Teide tempts you.
I have one day in December where I can ride in Tenerife in Dec
I've had a look at some of the links above, and it looks like I'm staying on the West side of the island near 'Playa San Juan'
Any recommendations for a nice 4 hour sojourn?