Anyone know the best way to get from the Barcelona airport to the El Born neighborhood? Can we take the Aerobus?
Where in El Born? The airport bus will take you to Placa Catalunya, and you can take a cab from there. It is probably not far, so it won't cost much. I don't think walking down Las Ramblas with luggage is a great idea, so I wouldn't walk unless it is really close. The bus let's you off in front of El Corte Ingles and I thinkmthere is a taxi stand right near there.
El Born is the south eastern portion of the medieval city area, east of the Barri Gotic. If I were you I wouldn't get the bus, but instead get the train from the airport to Passeig de Gracia station. You can then get metro line 4 to either of the two stations in El Bron: Jaume I or Ciutadella - check which is closest to where you are staying.
We took the airport shuttle to Placa Catalunya. We stayed only a few blocks from there. If nothing else you could catch the relatively cheap airporter then catch a cab if it's too much to walk. There is also a train/metro connection into town that is cheaper, but more inconvenient, than the airporter. We walked right to the shuttle so figured it would be easiest to just take it.