Check here for festivals and events in Gran Canaria when you are in port.
At the heart of the Vegueta quarter sits the twin-towered Santa Ana Cathedral, the first artistic construction in the Canaries, which was executed following the orders of Catholic kings after Gran Canaria was conquered in 1478. The construction started around 1500 and was not completed until almost four centuries later, making the intervention of several architects and artists inevitable, the result of which can be seen in three basic architectonic styles: Gothic, Renaissance and Neoclassic.
Another fun thing to see is to watch the "kinnetic" moving sculpture at the entrance of the Technology Museum which is only about 150 meters from where you are docked. No entrance fee required to see his sculpture.
Hop on/off buses are awaiting you close to the Terminal. As things slow down between noon and 3 pm this might be the best time to hop on.
Taxis: Just look for eggshell-white cars with a red stripe on each front door. Other signs that might help you recognize a taxi are the letters SP (meaning Servicio Público) and a green light on top or in the front windscreen (this green light indicates that the taxi is free).
A four hour taxi tour costs abour 100 Euro. The driver knows all the nice places.
Beach: north of the city (take a bus or taxi from Parque Santa Catalina) is the PLaya (=beach) de las Canteras, a 3 km stretch sand with lots of restaurants and a good local atmosphere.
Playa del Inglés, a 50 min ride by bus or taxi, has nice beaches too, besides the many high-rise hotels.
Arucas is the island's banana capital, west of Las Palmas into the mountains.
Besides the port is the El Muelle, a commercial center with large stores and boutiques.
The best places to eat are along Playa de las Canteras and Vegueta, the oldest part of the city, and in the Triana District.
El Corte Ingles an upscale Department store is more to the left from where you are docked. Just look for the "Casino" sign, it's right there.