Following up... I really loved the Acta Atrium Palace. It was within walking distance to Las Ramblas, Placa Catalunya, and even Sagrada Familia (a bit more of a walk, but still), but it was not RIGHT ON the mess, so it was pretty quiet as well. Nice room with a little sitting area/alcove type thing. Fantastic staff who have recommendations and are super helpful. There's an optional breakfast (I think 14 euro?) but I didn't partake in that.
ETA: I booked pretty far in advance. I did my booking through Expedia and pre-paid - so all I had to pay was the city tax that was around 2.5 euro for 2 nights.
Would love to hear more suggestions. We are arriving a day early and staying two nights after the cruise. I was thinking somewhere near the port for the first night. Then somewhere more in the center of attractions. Anyone stay at the Eurostar at the Marina? Hotel 1898 looks so cool for after. But there are so many choices!
I have stayed at the Eurostar Grand Marina three times now. Twice the night before the cruise and once for 3 nights after the cruise. It is a very modern hotel. The rooms are large, breakfast is lovely (champagne is included with breakfast), the pool is on the top of the hotel and it would be nice if it was bigger but is not a deal breaker. The stop for the HOHO bus is right outside and they always have plenty of taxis waiting. The journey to the port is less than 5 minutes and to the airport around 20 minutes. We have eaten dinner in the restaurant there once when it was pouring with rain and we couldn't bother to go out again, the food was good and the price not bad. It is not a cheap hotel but i would definitely recommend it.
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