A pergola would be perfect for your space. Search the box above under Photos for ideas.

I would love to see a table and chair set with a great umbrella. It's going to help soften the wood from your home and the stone from the patio:

What direction does the back side of the house face? Do you get evening shade as the sun sets?

Get some landscaping, an umbrella table and chairs, and keep the fire pit area open for summer evening fires. Even a strategically placed tree would give you shade but keep things open for camp fires. Decide on a tree based upon the size of it in 20 years.

A very nice table set would do wonders! http://www.bargainbacker.com/Outdoor-Furniture_c_346.html

Get a table and umbrella. Make sure the umbrella is big and can bend (ie the pole bends so you can move the umbrella to shade evening sun. You may want a small railing if you put your table near the edge (likely), so if someone tips his chair back, he doesn't go over. You should put a tree near the steps. I like lilacs, but depending on how much shade you need, and your budget, you might want to go for something that grows fast. But, of course, depending on the exposure, that might not provide the shade you want.

I'd put a border to soften your stone platform. Something easy and tall, like Perovskia (Russian sage), might do.

You aren't going to get really good advice without a discussion of your zone, the direction your house faces and your maintenance level. The best way to find plants is to stroll around your neighborhood and talk to neighbors with plants you admire. Most gardeners are happy to talk to you if you express admiration for their garden. Pay attention to what blooms when. A lilac will look pretty average when not blooming.

Unless you need it for access, I'd plant up the small area between patio and fence on the left.

It appears that the perfect place for an arbor/pergola is on the left side . A decorative screen could be incorporated into it to give you privacy and a flowering vine planted to climb over it would be attractive. Plant shade trees in the area that will block the sun when they are mature . I think that a built in bench for extra seating around the perimeter of the deck would give it a more finished look .

Plant a tree on the west side of the patio for one. Looks like you need a railing for safety so add railing with some screening . Keep it low on the left side. Create an outdoor room with covered patio on right and privacy screen. Check out privacy screens in Houzz photos for more ideas

Shade sails.

You could add a small shade tree to the side of the patio where you would like to spend the most time. This will take years however to grow substantially for shade. A pergola might work but it will take the focus from your bay window. I would stick with an umbrella and seating for now, until your tree matures. Also could add some arborvitae shrubs to the sunny side to shade but these need replacing every ten or so years due to splitting issues. Pine trees would also do. I would add softer shrubs on the other sides for privacy such as hydrangeas or other flowering shrubs for your area. Good luck.

Hire a local Landscape designer, the right trees in the right place would be a good start, adding some native plants in the yard around the deck should cool down the area both vusually and physically. Add several stone planters loaded with colorful annuals. Someone already mentioned a pergola, it will fit nicely with your paversand add seating under the Pergola for those desiring shade. Place some lounge chairs near the edges of the deck. Places benches around several edges with a stand alone water feature such as an Aquascape basin fountain close to them.
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A combination of some of the ideas above would really add to the look. I do not care for just one alone.

I didn't notice the sidewalk from the patio before. Where does that lead?

@ Darzy - we get no shade in the Summer. As for trees - our HOA committee will not allow anything over 20 ft. @ Dar Eckert - the path goes to our parking pad/garage. Thanks for all the ideas.

A dining set would be great to the right and some comfortable deep seated chairs or similar would be a nice touch around the fire pit.

Hi Kimi - We were thinking that a white pergola would look great over this area. We also think that some conifers in pots at the end of the patio would add some privacy. We put together this quick 3D image as a possibility of what could be done - Let me know what you think !

The Before...

The After

and another similar option being less dense and allowing more light through...