If you want a clean modern look I would keep open storage to a minimum with only special pieces on display and everything else behind closed doors . I love the Besta line from Ikea for storage solutions it is very flexible to suit any space and has a clean modern look that would work well in this space.

Get a sectional. (Anything from a modern sleek sectional to something a little more comfortable but still clean like Pottery Barn's Solano sectional--but likely smaller). Do NOT put it on the wall as the photos show. Bring it further into the room. Put a sofa table behind it. Overstock and Wayfair are good resource for well-priced quality sofa tables. Add a modern sectional lamp (similar to the one shown). A sling chair would look nice. Look at allmodern.com for ideas. It needs a larger dining room; again, clean lines. I'd put a bigger chandelier/dining light in as well. I'd add a large rug to warm things up. Either a solid-color shag type rug or an over dyed type rug would look nice.

And, I like the decor you show. The gallery wall will look good, not too much.

yellowginghamdoll - Thank you for all the ideas! I'd prefer to stay away from a sectional because the coffee table won't be centered, plus I'm worried about covering up part of the light (from the sliding door). I have a cream colored shag which I plan to use. And my dining table is much bigger. I'll look into the sling chair.

Patricia Colwell - Thank you! I just looked up Besta and it's great. I'll definitely use it in the dining room.