It does seem kind of a random arrangement. Have you looked at patio photos here on Houzz? Many may be more elaborate than you want, but pay attention to the use of space and arrangement of elements to better inform your own design.

Additional thought. In our studio recently, the owner and our other designer were giving me the business asking me if I was allergic to curves or arc and tangent design since the overwhelming majority of my patio designs are rectilinear. I pointed out that when indoor rooms are octagonal, curvilinear or ellipitical I would consider taking those shapes outside as well.

I mention this because I noticed you have an octagonal space for the fire pit with a round fire pit. Those shapes, in this case, are in conflict with each other and the fire pit space is in conflict with the kitchen and pergola space. Just like inside, the furnishings and decorations will provide definition and interest for your outdoor living.

If you are positive you want a round fire pit, here is a round one with a circular patio that we are in the middle of working on. It's more harmonious than a circle contained within an octagon. Again, good luck with the patio. Post some photos when you finish.

Do you have a photo that shows the back where the patio will go?

Seems like you have three functions: a shaded dining area, an outdoor grilling area, and a fire pit. I had all three on my tiny patio at my last house. I didn't catch your zone, but I guess I'm having trouble figuring out why you've left the grill out in the open. We often wanted to grill outside in our temperate zone and I had to put a patio umbrella over SO, since we never had the time or money to install the pergola that I wanted. Also, important to place the eating and grilling area near the doors since you don't want to be carting food around all kinds of obstacles from the kitchen to the outdoor eating and cooking area. I have an obstacle course porch in my current home to navigate around before I get to the grill, so I'm aware of that issue. Although I am also aware of the issue of not wanting the grill too close to a door or window so that the cooking smells don't waft into and overpower the house.

Lastly, the fire pit could be surrounded by crushed stone or even "gasp" pea gravel if it was located well away from the house to avoid the dreaded gravel creep. I've even seen people use sand. None of those ideas are my ideal, but something to consider. You might want to consider installing your patio in stages and use a portable fire pit in the meantime. We had one and it only took up space when we wanted to sit around the fire, which was a way less common occurrence than our eating out, which was practically every night during good weather. We still use the portable fire pit, and my fire pit area right now is just a scrubby grass area of my lawn for our occasional fires. I live in a mosquito zone, so my fire pit time is limited to about four months tops. YMMV.

some ideas

That's a knockout option that Doug posted for your space! At the risk of sounding like a broken record, "different spaces for different purposes" always makes sense. Doug's rendering exhibits that principle. Again, good luck and post some photos when it's complete.

Thanks John,,,I'm a fan of your design aesthetic, as well.