For me, the trip to Teide/Las Canadas is simply unmissable. I used to work with a person who had visited Tenerife a number of times and I was totally amazed when he said to me one day, 'Isn't there a volcano or something there?' He'd never ventured further than the hotel pool.
Also, I agree the drive over to Icod, Garachico, Masca & Punta de Teno etc. is another unmissable. Another fantastic area scenically is the Anaga mountains in the far north beyond Santa Cruz.
I haven't been to Loro Park for a number of years but remember having a great day out there some years ago.