What do you like? Traditional? Mediterranean? Ultra Modern? Country? Contemporary? How old are the children? Boys? Girls? If the children are young: http://fineartamerica.com/profiles/1-sharon-cummings.html?tab=artworkgalleries&artworkgalleryid=258335

If they are older: http://fineartamerica.com/featured/dusk-float-sunset-art-sharon-cummings.html

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This room feels contemporary.

I'd get some graph paper, draw out the rooms, then cut out some furniture...or try downloading some free software and moving around some software to see how it will look. I'd go for a transitional look. Unless you already have all your furniture...but yes, it has more of a contemporary feel.

Ahh a blank canvas, I love it.have to say the living room looks like it's crying out for a sectional!
It's the nicest sofa style to use in a large open plan room I feel. Have it facing the tv rather than against the window.

Are the dining room walls a slight grey colour? That earthy putty colour is a nice choice to zone off the dining area and makes it more intimate.
I feel a nice round table would work well if you have enough room- maybe glass top so wouldn't dominate room?

Wow you are brave having cream carpet in a child's play room! Lol, in assuming they are fairly young as you've described it as a 'play' room.
In that case I would actually put another rug on
Maybe even circular to mirror the dining table?
That creates a 'focus' for the room where traditionally a piece of furniture would stand ( and if they spill anything it's a bonus because you can clean or replace it easily!
I wouldn't add much to the kids playroom... I used to love having the space to roll around!

Have a big trunk so they can dump their toys into it (remember an open plan space needs to be flexible and if you can't shut the door on th playroom at least you can dump the toys in quickly!)- maybe an ottoman style seat so can double up as seating.
I would use decals on wall to make it more childlike and brighter... Which are then easy to change or remove if you need a grown up space again.

These would be the big purchases that would zone and anchor the rooms... Once they are in place you wil have more of an idea how to accessorise the room. The fireplace wall certainly needs more oomph!