Since the living/family room is the gathering space where you probably spend much of your time, you'll want to create an especially cozy and welcoming feeling here. Fabrics that beg to be touched in rich, warm colors are instant soothers: fleece, velvet, chenille, velour, satin.
There are a great variety of inexpensive throws and blankets available in these cozy fabrics-drape them artfully over the backs of easy chairs or the arms of the sofa. Obviously, you don't want a satin-covered couch around kids (not to mention what a hard time guests would have staying put on it!), but a small, satin-covered throw pillow might be just the thing to wrap your arms around or rest your head upon when you're curled up in a chair or on the sofa. One really luxurious velvet pillow mixed up with several smaller throw pillows is also a nice touch.
Create a feeling of instant ease with a reading area. If space permits, designate a corner of the room for this purpose. A comfortable chair, a floor lamp, a small table holding a stack of books (with room for a snack or a cup of tea) are all you need to create a mini-oasis in this busy room. Other touches to include are a footstool or cushy ottoman, a cozy throw or afghan, and a magazine rack.
A game nook is another easy and fun way to invite people to sit and relax. You could designate another corner of the room for this purpose, or you can make it the centerpiece of the room. Arrange a couple of chairs around a small table with a chess, checker, or board game all set up to play. You could keep a storage bin or small toy box nearby, stocked with more games, decks of cards, and small notepads and pencils (for keeping score in those hot games of gin rummy!).