Do you live someplace warm? I wouldn't mind it so much in FL or TX, but this would leave me so cold up here in New England.

Take a look at the stuff that Candice Olson does on Divine Design. She does an excellent job of making contemporary spaces look warm and inviting by mixing in textures, colors, patterns and a nod to the past.

The curtains are not the first thing I would do...though they could be changed. I don't understand the furniture placement re the sofa and the doors. I would love to see a credenza or something to anchor the space under the TV and some chairs facing the sofa so that it becomes more conversational, pulled together with an area rug.

All of the accessories in the space are hard....the wooden poles, the rack with the bags on it, the glass topped table, the frameless art. The space needs some softness to be welcoming.

The inspiration pic is lovely...it adds more color and a lot of texture. Note too the importance that lighting plays in the space....

I love the way it is really. It looks very nice and modern. But yes, the curtains have got to go. It makes the place look too closed in.

I love how carefully you have edited, and now you need to add a bit more life.

First, the wet bar...I think you need to loosen your grid a little anyway. If you can swap the fixture over the dining table with the pot light that falls between the two sliders, you can move your dining table toward the family room part to sit centered on the wall, and put the wet bar against the wall where the four pictures hang, to the left of the hall door. That would bring your whole open plan into a more integrated arrangement, and put the wet bar adjacent to the fridge and the bar counter.

As to warming it up - the traditional way that the Modernists warmed their designs was with ethnic textiles and pottery. I think a couple of beautiful tribal rugs - or if that's too much look, a natural fiber rug and some pillows made of tribal woven cloth - a natural wall covering behind the television (a really good nubbly grasscloth would be easier and softer than the stone of your inspiration), and perhaps a coat rack made of natural branches rather than stainless would be good choices...?

I like the walls. But in combination with the floors (terrazzo?) it's a bit much.

The TV is floating. Anchor it with bookshelves on the TV wall, or similar sized art in black frames and a buffet under it. That could be the place for something not-modern as an accent, either carved, painted, or ethnic.

A rug under the coffee table and a couple of armchairs facing the couch for sitting and chatting. If the rug is hand-made it would soften the ice-palace look of the floors a bit. Persian, Navajo, kilim, or something ... just not-modern.

A area rug in the living room would help, maybe sisal same color as the cushions in the living room. Since you have some yellow in the pic in the dining room I'd be inclined to use that as the accent color in the living room. Yellow pillows on the sofa, a yellow chair and/ or a brown chair same as the cushions on the sofa with a yellow pillow or even a black chair with a yellow pillow and a yellow wooden dresser/buffet under the tv. I'd even consider putting yellow drapes up with a bold black trim or print on them.
If I had to pick and chose where to start I'd start with the windows. They are going to set the tone for the rest of the room.

Definitely and immediately a rug! Perhaps one of those patchwork hides or something with a nice clean narrow stripe:

I have to say the 'bones' of your room look great, very well done and true to your modern aesthetic, but as others have said a touch too cold.

I also think you are on the right track to nix the drapes, they are a little too basic, I think you need some blinds something without layers or fuss, just flat sheets of colour. Or if you want the volume of fabric how about sheers where the hardware is minimal or non existent floor to ceiling.

Your idea of stone would add another warm wow element that could work. But other options are brick or even wood flooring on the wall. It's a stone alternative and would perhaps balance the dark kitchen on the other side of the room. As others have said lighting should be key here floor and table lamps. It can stay modern (or at least transitional) but become quite cozy.

[Contemporary Family Room design[(https://www.houzz.com/photos/contemporary-family-room-ideas-phbr1-bp~t_720~s_2103) by Baltimore Architect Ziger/Snead Architects