Bacelona

After spending a short three days in Barcelona, the site I enjoyed the most was Sagrada Familia. I was expecting to enjoy it - but it was so much more amazing than my expectations. Be sure you purchase your tickets in advance or you could spend a very long time just waiting to get in. Two more things I really enjoyed were the Boqueria and wandering through the Barri Gotic area. Be aware that this is very subjective and that I really didn't do the city justice in three days. I would recommend you read a couple of travel books or research on line to get an idea of what appeals to you most.
Unfortunately, I felt I really didn't scratch the surface of Barcelona in 3 days, so be aware that one day will go very fast and leave you wanting much, much more. I enjoyed Barcelona more than I expected and would love to return for at least a week.....

I agree that the Sagrada Familia should be at the top of your list. Also, if you want to cover a lot of ground, do the "hop-on, hop-off" bus tour that has two lines. One ticket covers both!

We signed up for the Fat Bike Tour, and absolutely loved it. So much fun and a great way to see all of the major sites.

Sounds like a day off the cruise ship. When we are new to a port we work from the general to the specific. Generally we take a hop on/off something (bus, trolley, etc,) and ride it around once just to see what we would be more interested in seeing in greater detail. The three top things depends on your interests. Your cruise ship will most likely dump you at Columbus Monument if not using the cruise port. From there walk up Las Ramblas to the Placa De Catalunya and the TI. The hop on/off buses leave from the east of the Placa and it is obvious. The TI will have a lot of different walking tours that are available at very reasonable prices. From there you can decide what are the most important things for you to see.

In one day, I'd take the Barri Gotic (Gothic District) walking tour available through the TI (as I recall starts at the TI in St. James Square). Then metro over to the Sagrada Familia to see some Modernist architecture. On a tight schedule you can save time and money (blasphemy) by only walking around the outside. They've made progress inside, but it's still a construction zone. Unless you take a taxi, you probably don't have time to see Parc Guell or other Modernist architecture, so metro back to Placa Catalunya and stroll the Ramblas until it's time to be done.