Best hotels near cruise terminal

Hotel Lleo is located half a block from the top of the La Rambla. We found it to be very clean, modern, breakfast was included, roof top pool and recommended by Rick Steeves.
We stayed 3 nights precruise and would definitely book there again.

For transportation, we purchased a T10 ticket (~$11) and took the Renfe train from airport (T2B) to Playa Catalunya. That ticket is good for 10 trips on Renfe and Metro, so the trip cost two of us about $2.20. We returned to airport by taxi, and cost 45 Euros!! It was faster, but at a steep cost.

TripAdvisor might also have some ideas.

DO NOT choose the Hotel Miramar. This was the most unclean and nasty hotel we have experienced in over 20 years. Most staff were friendly, but manager was extremely rude. Was promised room at 1:30, but manager stepped in and said no, would have to wait until 3:00. We had already been waiting since 10am, and had requested an early check in several weeks in advance. When we got the room, it was filthy, toilet had urine stains on seat and floor. Shower and vanity had not been cleaned in a long time. Bath towel was rolled up and wet, like they just rolled it up after last guest used it. Room was disgusting everywhere you look. Every door had a problem working correctly - shower, WC, refrigerator, and balcony. Manager had checked our bags, and when room was finally ready said that he would bring up bags immediately. Almost 2 hours later, bags had not arrived. Went to check on bags and manager acted as if he had never even spoken to us before and just pointed us to the storeroom where I had to find our bags among all the others and carry all five of them up myself, without even a cart. This would be a terrible place to stay even if it was free.