We have stayed in a couple of different hotels in Barcelona, but have decided to stick with TRYP Apolo this year. We always seem to get an excellent price, which is a plus. The location is perfect for us as it's walking distance to Las Ramblas. Hotel is spotless, great air conditioning, and the rooms are very spacious. Always seems to have a lot of cruisers staying there. It's about a 5/10 minute drive to the cruise port.
Just another note to add, while it is only a short drive to the cruise port, I have seen people walk to the port, and while it absolutely can be done, it wouldn't be something I would recommend. It's a really long bridge to walk over, and I've seen many families struggling with their luggage in the heat. Each to their own of course, but you'll see what I mean when you're heading to the port yourselves!