Not sure about the taxi fare but by my calculations it is about 35 Kms from Santa Cruz to Puerto de la Cruz. You may be better to take the organised tour to be sure you get back in time for your departure.

I have always found Admiral Travel to be the most reasonable when it comes to excursions.They are a British run Excursion and Travel Company who are based in Tenerife.Not sure if they have outlets in the North,but well worth checking out before committing yourself.Hope this helps
Caroline x