You will have to try hard to find a better location. It is close to shops, metro and las Ramblas and there are restaurants all around. It was very easy to get anywhere - a couple of stops on the metro to the beach or Park Guell and walking distance to most things.
The apartment is on the 5th floor so there isn't any street noise at all which we were concerned about being right in the city. There were a couple of protests on whilst we were there and you could hear it but it wasn't an inconvenience at all and was over before 9:30pm.
There is a lift (small) - or if you have eaten too much paella and drunk too much wine the 133 steps to the apartment were a great way to walk it off. The bedrooms were large and comfortable and each room had its own ensuite.
The kitchen had the necessities but it was just as easy to go downstairs and find a local eating place.
Check in was easy, we were met at the apartment and given keys and a tour of the apartment and facilities and David and Eike were contactable by email or phone immediately (if for instance you get mixed up and tried and get into the wrong apartment building - warning the one immediately to the right looks exactly the same).
There was also a Spanish phrase book and Spain Lonely Planet book which were of great assistance.
We had a great stay and were very comfortable.