It all depends on what part of the Eixample area the loft is located. The good news is that the Eixample district is right next to the Ciutat Vella district where La Rambla and Plaza Catalunya is located and so if you're lucky, you could be no more than a 10-minute walk away. The beach is another story. I would say you would be at least a half hour walk away, again depending on what beach you wanted to go to. However, I wouldn't be overly concerned because Barcelona has a very good public transportation system, underground subway and overground buses and trams. Visit the following website for a clickable and zoomable map of Barcelona that may help you locate the loft you are interested in. Have a great trip.
http://www.bcn.es/guia/welcomea.htm