We were in Tenerife in December.
It was a beautiful city. We walked around. Even found a Marks & Spencer store near the park in the centre of town. We didn't go, but apparently they have a beautiful parrot enclave.
There was a free city museum with some nice art exhibits in front of the park. And near the ship there is a hidden (free) museum underground that shows you the old battlements. (Not for the claustrophobic). Most people missed this one as it simply appears to be a set of stairs going down from the plaza.
The city also has some beautiful statues all over town and in front of the theatre. And a nice open air market called La Recova.