Look at furniture configurations on any number of outdoor spaces here on Houzz and you will see a wide variety of arrangements. While you may not find a perfect match for your situation you'll certainly see enough to move you in the right direction. Invite friends or family over and see how you utilize the space and you'll probably get an even better idea of how to arrange it.

10' is about 2' short of feeling like what's necessary for patio furnishing. Consider bordering the patio outside edge with a couple more feet of paving. It could be matching patio or it could be a contrasting edge, like many patios have when they're newly built.

Whether it is the new or old furniture, consider drawing a plan on graph paper of the patio, then making to-scale, plan view paper cut-outs of the furniture pieces. You can easily move them around on the plan until you achieve an arrangement that works well. 1/4"=1' is a good scale to use for this.

When it comes to the patio "feeling inviting" it probably has more to do with the surroundings than the patio surface itself. Are there good views to look at? It looks like you could use some beefed up landscaping.

Your siding looks like it’s being damaged by the grill.

10' is about 2' short of feeling like what's necessary for patio furnishing. Consider bordering the patio outside edge with a couple more feet of paving. It could be matching patio or it could be a contrasting edge, like many patios have when they're newly built.

This is a great idea.

Additionally, you have a lovely yard and nice furniture, but I think it's looking kind of ho-hum because it needs a pop of color -- I'd lean towards red, but blue would also look nice. I'd consider spray painting the furniture. I think that'd make a bigger difference than rearranging the furniture.

There are simply too many things here to comment on (why waste time telling you how to configure that furniture when you're going to buy something else). So all that I will say is .... when you have two couches they need to face each other and they should run in the opposite way of your house. So I would put the two couches facing each other as they will fit perpendicular in front of the sliding glass door so that when you walk out that is the main seating configuration that you see. And then I would go from there in terms of placing any other pieces. And I would not get a sectional couch as your space is not big enough for that. Get smaller pieces that can be moved around as needed. I would concentrate on creating two spaces ... one for conversation and one for dining if the goal is to start eating out there more, or if not then create two conversational spaces. If you're going to do the two couches in one area, then get 4 chairs in a circle with a fire pit/coffee table in the center for the other area.

^That was the first thing I noticed too, the damaged siding from grilling. Please move the grill to a safer location away from the house. It doesn't need to be far away, just not right up against the siding. this insp pic shows a rock wall behind the grill but it's away from the house siding.

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I agree about the siding. As for funiture the stuff you have is far from welcoming it does not look comfortable. The comment about drawing the patio to scale and playing with cardboard cutouts of the furniture you are planning is always a fun way to get the right pieces.It certainly wouldn’t hurt to enlarge the patio a bit and make the dining area a bit more welcoming with some color like maybe a bright colored cantilevered umbrella and then that same color for cushions in the sitting area.

Some ideas based on Yard's idea to expand the patio with a border:

partim great suggestions....