The current rug in the center of the deck seems to serve no purpose. I'd remove the little half-moon mat--it's jarring to the eye--and pull the rug all the way to the doorway where it will do some good.

The problem with umbrellas is they aren't much good for decor because you really can't leave them open when unattended. One good gust of wind and they'll be over the deck or smashing through the window.

You might look into a shade sail which could add a spot of color and be left up all the time...

NO Equal Design Shade Sail · More Info

Pool Shade Sails by Tenshon · More Info

...and then finish the space with lots of plants in pots.

The problem with the shade is that it needs to be customized to fit that space. Can I get a non custom shade sail for the same price as an umbrella?

I would head towards a more natural feel, due to the surroundings. I would move the dining table over to the side with the bbq and place two chairs/coffe table/rug there instead. My brother has the type of umbrella in the photo below and it's great. Glam and interest is achieved with pillows, rug, accessories, lanterns, pots/greenery, candles, etc. Make it a destination vs just a place to eat.

outdoors · More Info