Sound is absorbed by soft materials such as area rugs, drapes, large canvas artwork on the wall, soft furniture, etc. You might try two large area rugs under the living and dining areas (bigger than the one you already have) and drapes or roman shades on your large windows. Maybe some artwork too.

Thanks, indeed. A rug would be an option, but our 2 small kids eat like pigs... This option is for later :0)
Does anybody have an idea that fits our minimalistic style? We are not fan of "busy" spaces. Is there any technical solution? Sth we could stick under the table or a trick, magical plants perhaps?