One of the most beautiful city in Europe. Good public shuttle service from the port to the center, you don't need taxis or organized shuttle. If you embark,take a taxi from the airport at less then half price (for a couple) compared to royal caribbean shuttle. You can just spend your time strolling the ramblas up and down or be more organized and visit a few of the dozen of worthy tourist points of interest.
Another great european city. Take the public tram from the dock to praca Comercio. There you are in the city center, shops, restaurants and so on. You can take another tram to the castle (n18) with stunning views all over the town, or take the elevator to go the Bairro Alto. Another public tram takes you all along the river (further than the docks) to the attractions of Jeronimos Monastery, Monument to the discoveries and Tower of Belem. Don't miss any bakery to eat the Pastel de Nata, unique in the world.
Hire a car and go around the island. Wonderful landscapes. Head to the Teide Volcano and try to get to the top. Santa Cruz de Tenerife is a pretty town but there is nothing to visit. You can also try the beach. Against expectations, beaches are not the best thing in all Canary Islands, but near Santa Cruz you can find Las Teresitas beach, one of the bests. Especially if you get a nice day during winter, you will feel excited to sunbathe and swim when everywhere else in Europe is so cold. To Las Teresitas take a public bus from the port. It's 6km away, ask a local.
The most beautiful city of the world. You can take the public bus 177 from praca maua'. It will take you along the center and all the beaches like flamengo, copacabana and ipanema. Get down to ipanema and then walk back to copacabana. In one day stop, take a taxi in the morning to the corcovado mountain and enjoy the most amazing view of the world from the jesus christ statue. And then go to the beaches of Ipanema or Copacabana. At the beach take a shrimp stick from a vendor and a frozen beer.