It's pretty important to know where you are located as well.

If in SoCal, growing grapes would be an immediate place to start :-) I'd look into constructing some sort of pergola as both a support system for the vines as well as offering some shade for that very open patio area and creating some privacy

I'd also consider removing what appears to be a very weedy lawn (and a water guzzler) in favor of expanding the planting beds and bordering/connecting them with gravel paths (decomposed granite?). Include drought tolerant, Mediterranean type plants in the planting beds - salvias, lavender, rosemary, echium, euphorbia, etc. Maybe include a half oak wine barrel planted with a dwarf olive tree.

You might also want to think about some sort of wall-mounted water feature on that expanse of fence, like one of the fountains shown here. These are very characteristic of an Italianate or French country garden one would find in wine country.

What pergola would you suggest? Any suggestions if we want to incorporate wine barrels?

Whatever pergola style you prefer and suits the architecture of your house. That link offered a variety of styles - italianate, Arts and Crafts, rustic, Asian or just very basic.

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And I did suggest something for the 1/2 wine barrel :-) But filling one with a colorful flowering plant - like zonal geraniums - would be appealing and appropriate as well.

Whole barrel ideas?

Do you think a narrower pergola look good like along side of yard or by wall?

I can't see the yard clearly in its entirety to be able to advise. It would be logical to construct the pergola adjacent to or covering the existing patio, to provide both shade for the seating and some privacy.

And I'm not sure what you would do with a whole barrel other than using it as a table base. Or cutting one in half lengthwise and using as a bench.

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I was just thinking a pergola over patio concrete and then down side of yard to left over dirt area

If that's what you want, go for it :-)

This is not to counter any of the advice you've received so far, but to add to it. This is a suggestion for one way to divide the planting area from the lawn area if you are keeping with the basic plan of patio surrounded by planting. The lawn could be shrunk. If desired the shrunken area could be swapped out for granular "paving." Or it could be VERY low, steppable groundcover (If such a thing exists where you live.)

Thanks. We would like to incorporate abit of wine theme

How about making a low wall with wine bottles? A google search on "wine bottle retaining wall" will bring up pictures.

"Wine theme" can mean different things to different people. I think of France and Italy's ochre plastered walls, decomposed granite paths, herbs and olive trees, as described by gardengal above. But there are also more rustic American versions of a wine theme, flowery romantic versions, and more polished urban takes on the theme. Could you elaborate a bit on the theme you have in mind?

Comfy chairs made from wine barrels: http://www.visitcalifornia.com/attraction/central-coast-wine-country

When I mention wine theme I am thinking of showing our interest of wine and wineries throughout the yard. I know I like the integration of barrels somehow or possible yard decor. Hope this helps.

I'm more of a barrel and fermentation guy as I make wine at home

Wine barrel water feature? Just Google those words - lots of hits.

Wine making seems to be celebrated mostly as an indoor sport as far as décor goes, but some of the wine cellar themes can be adapted to outdoor use, with some applied imagination. http://www.houzz.com/photos/query/outdoor-wine-barrel-decor

Wine Barrel Light I'd saved this pin for a $900 wine barrel light as all you'd need is to be handy with a drill to do your own (that said, I haven't made it so could be underestimating).

My neighbor in Newbury Park had one of those grid roof thingies, and it was covered with grape vines/ grapes that then hung over the sides as well. It looked real nice and provided shade. Should work in Irvine as I dont think Irvine is that much warmer than Newbury Park. Just make sure they get enough water. Half barrel planters are another idea.

Attached are some pictures showing the back of our house and side. We would like to incorporate a patio roof and jacuzzi into patio area. Does anyone have suggestions?

You're doing great. Once empty, there are all kinds of hacks for using wine bottles if you are into working with glass. My husband is a wino and I've contemplated incorporating them into a garden wall. Google "wine bottle garden wall" or "wine bottle garden fence" for lots of ideas.