Madeira is a nice destination, and if you don't want to do one of the ship's excursions, there is an 'on/off bus which leaves from the road into funchal from the docks. It's an all day ticket, on and off . .it takes you up to a viewpoint from where you can see the whole of funchal, and the house where Ronaldo was born if you are a football fan!
Santa Cruz is quite a nice city to wander around. Otherwise take an excursion to Teide to see Spain's highest mountain ( a volcano) or go south where the sun always shines. Puerto de la Cruz is the oldest tourist destination on the island, and is good for shopping, wandering around etc.
The town of Arrecife has nothing much to appeal to you. Shuttles usually run to Costa Teguise and Playa del Carmen, typical tourist areas which have sprung up in the last twenty five years. Lots of bars etc. beaches if the weather is nice. Otherwise, take a trip to the fire mountain which is more interesting.
Beautiful island, but the capital Santa Cruz is small and after an hour or so offers very little especially on a Sunday when the ship docks here. Los Cancajos is the nearest decent beach . . You can get a taxi there quite easily, or go to see the huge volcanic crater. Twisting mountain roads on the way, so be prepared.
The ship docks within easy walking distance of the city. there is a modern shopping centre as soon as you leave the ship if shopping is your forte. otherwise, walk through the town to the very pleasant beach (about ten minutes) A lot of people on the ship were qjuite unaware that this city has a beautiful beach with plenty of little bars and restaurants on the front just ten minutes walk from the ship!