Hmmm, yes, I think a large area rug would help define the family room space. Don't be afraid to float a sofa, it can help define the space as well.

I would begin by defining the spaces. Rugs would be a good start. I would put one large one in the family room space and then put another one under the dining room table. The rugs shouldn't match but they should complement each other. I would think about painting the entire space a pretty, light color that works well with the flooring and kitchen cabinets. It doesn't look like you have a chandelier over the dining room table. A light there would also help define the dining space -- something big and modern would look great there. Given that you already have the large, darkish furniture, I would think about trying for lighter and brighter accessories (glass and metal coffee table for instance.) Think color to modernize the space.

As Kelly Nelson said, paint the space a lighter brighter color, one consideration would be something like a blue gray or grayish green. As has been mentioned, rugs under the dining room and living room areas would help define the space and could be a place to introduce color and pattern. Drapes as well for the doorwalls and windows. Color and texture in the accessories for the tables and furniture. Some possibilities for wall decor would be a gallery wall in the living room and perhaps a mirror on the dining room wall.

Dining table looks a little cramped. I would move it so that it is centered with the wall holding the model ship.

I would move tv to where the large sofa is. Float that sofa out, facing the wall that now holds tv. Of course, you need a great built in unit to hold tv and accessories. Matching the cabinetry to the kitchen would be nice. This way you can watch while working in the kitchen.

The area where the tv was can hold a small pub table or desk.

Warm up the room with the addition of large area rugs. You have a great space to work with!