Luggage storage In Barcelona

Its called "Left Luggage". Here's one link I got when I Googled "Left Luggage Barcelona"

https://www.barcelona-tourist-guide.com/en/transport/baggage-storage-barcelona.html

I believe the typical airline advice for transatlantic flights is to be at the airport 3 hours before scheduled departure time. I flew home from Barcelona in 2016, and I was in the United check-in line for about an hour. I made my flight, but I needed essentially all of the 3 hours I had allowed. I think by the time you check a bag somewhere and set aside time to retrieve it later, you won't really have enough extra time to go anywhere except to the airport, even assuming you actually get off the cruise ship when you expect to.

The most I'd plan would be paying a taxi driver to drive me past a few of the key modernista sites on the way from the port to the airport.

Agree with acraven here, at most I would just pay a taxi to drive past the main sites before going to the airport. That way you can get a quick taste and then return to Barcelona on another trip for 4-5 days to do the city proper justice :)

Sorry I didn’t give enough info.
The intl. flight departs at 3:30pm.
Plan to be at BCN at 12:30p. Still leaves the morning as cruise is over at 6:00am

I don't know how many of you there are. The larger the party, the more it makes sense just to take a taxi to the airport. I was very happy with the Aerobus, which departs from Placa de Catalunya. If there's a luggage storage place reasonably near there, it puts you sort of in the middle between the modernista sites on the Block of Discord in the Eixample and the Barri Gotic. Either would be walkable unless someone has mobility issues.

La Sagrada Familia is a bit farther away, but public transporation is good (or use a taxi). If you want to try to go inside one of the best-known modernista sites, you'll need to buy your tickets in advance. They are not cheap; I have no idea how accurately you can predict when you could arrive at your first stop.

If you're not comfortable pre-booking something, a good option that you can generally just walk right into (after paying the entry fee) is the Sant Pau Modernista site. It's beautiful and consists of multiple buildings on landscaped grounds.

There's a possibility that you might be able to get into the Palau de la Musica Catalana without buying a ticket in advance. I haven't been there since they started allowing visitors to self-tour, rather than requiring everyone to take a guided tour. To clarify: There will still be an admission fee; I just mean that you might be able to walk up and buy a ticket for immediate entry, though I do not know for sure that it will work out that way.