Where can I find a place 24h open for eating and drinking near the seaport?

I'm not going to answer this directly, as I don't know the answer, however bear in mind that Barcelona only really comes alive really late at night and life goes on until sunrise. Therefore a standard schedule does not apply.

If it's the La Barceloneta area that you are referring to, there's a number of higher-end restaurants which serve sea-food. Most of those are rather tourist orientated, I don't know the food quality. It's worth getting a few blocks off the tourist areas in Barcelona, as the quality of all establishments improves quite rapidly as soon as you get off the beaten track. Always look for a queue of the Spanish, that's how you'll know the food is good :)

Camila,

I worked on a cruise ship too. We ported in Barcelona for two summer seasons. The main city is about a 20-30 minute walk from the ships. There are shuttles to make it easier and fast. At the time that I was working the bus would drop you off at  La Rambla,the famed street of shopping, and artistry. There are some great markets just off the side of the street. In addition there is La Barceloneta area. There are beaches and harbor side restaurants.

My two favorite things as a crew member are, 1) go to the Maremagnum Mall, there is a starbucks with wi-fi, and when I was there a couple years ago the mall had free wi-fi.

2) There are a ton of small cafes within the neighborhood of La Barceloneta which are neighborhood cafes, and not on the water. These tend to be super cheap and interesting as you're surrounded by locals and many times the main seating area is in the courtyard of an apartment building.

Make sure to take the subway places. The port is super close to lots of things but Barcelona is one of the best spread out cities in Europe. You won't run out of places to go all night.