Hi Trudy and Bob,
welcome to cruise-chat.
You can do Tenerife on your own. You can take a bus to Puerto de la Cruz, 40 minute ride, costs about 2 $ and you can discover this popular vacation area.
People from the tourist information are available at the pier and give you some good information. Indepent tour operators offer several tours around this beautiful island.
If you want to see more, take a half day tour, including the Teide Mountain and Las Canadas. It´s such a different landscape on this island, it´s a must see.
For the bus tour to Puerto de la Cruz you can read my website
and you´ll find it under the link Atlantik 2005.
We have visited Tenerife several times before (not by cruiseship), so we knew, what we wanted.
Hope you´ll have a wonderful time