We have stayed at Hotel Condal. Just a stones throw off Las Rambalas. We found it to be clean, cheap and pleasant enough for an overnight stay. Maybe a little noisy due to the location however not a big problem.
We are booked in for two nights again in April prior to our cruise on Brilliance of the Seas.
Have to say though also have stayed at Jazz for our Honeymoon. Excellent but pricey. Hope this helps.
This website contains a lot of info on the cruise/harbour area http://www.barcelona-tourist-guide.com/en/transport/barcelona-cruise-port.html We do have delegates attending conferences in Barcelona and most like the Hotel Jazz with lots of ways of getting about the cityty website http://www.hoteljazz.com/ hope this information helps.
We stayed the Ramblas hotel (which is, at it says in the Ramblas --near the bottom) This was booked for us by the cruise company (2 nights pre cruise stay in Barcelona) It was very good and reasonably cheap too. They were geared up for cruise customers and booked taxis to the port for everyone. It's not far to the port but the larger ships are quite far out so not really walkable (unless very fit and with no luggage!!)
If you're looking for really cheap and good, the Barcelona Travelodge can't be beaten (sometimes available for 20 euros per room) and it has a cafe for breakfast. at something like 4-5 euros Some distance from the port but not too far and taxis available. Hope that helps.
Have a look at Hostal Grau which is in a little street just off the top Las Ramblas. Room only but cafe downstairs for breakfast.