We stayed here http://www.friendlyrentals.com/en/apartments/barcelona/apartment-1121-1.htm It's not big enough for you but the location was great. 5 minute walk to the beach and 5 minutes to the ramblas the other direction.
Anyone got any recommendations? we need 3 bedrooms, either La Ramblas Barri Gotic or overlooking the sea. Loads of websites to wade through but hope someone might have stayed somewhere nice and central with plenty of "buzz" for the teenagers! Thanks.