Q: What is the best way to go from the cruise port to Park Güell? We only have one day in the city.
A: I recommend you take a taxi from the Cruise port to Park Güell. The journey is only about 15 to 20 minutes. In addition ask the taxi driver to drop you off at the car park at the top of Park Güell. You can walk down through the park instead of walking up (hard work). That taxi fare should cost around 15 euros for up to 4 passengers.
Metro: If you take the metro it will take you about 1 hour. From the Cruise terminals you would need to take the T3 PORTBUS to the Christopher Columbus monument (which is at the foot of Las Ramblas) Then you will need to take the green line metro from Drassanes and get off at Lesseps. You then have a about a 25 minutes walk, half of which is up a steep hill. This will only take you to the foot of Park Güell. You would then need to walk up through Park Güell which is quite steep. This is why I recommend it's best to take a taxi.
For further information on Park Güell including a location map follow the link below: