Our patio will be off of our small deck. The deck is rectangular. However I do want, up in the back (visible from the deck) a circular deck built into the grade of the land (which slopes into the property slightly). This will be a landing pad for a "hot" and cold tub. I don't need a pool, but I'd like to be able to jump into water after a hard days work (and I no longer use a tub indoors). Round is a shape that would work well up there so I originally was thinking of echoing that shape. As for pavers, I will use just the plain, cheap concrete style. Which may sound odd (so many people get rid of them) however, they are very 50's/60's and that is the look I am going for. Our furniture is coming from a friend, and it's all vintage. Our outdoor kitchen will not be (are you shocked?) what most people would have. A small adobe oven for baking, an "open" adobe "grill" instead of a typical BBQ and a side area with two burners - sort of like a vintage wood stove idea (I'm even thinking of finding an iron stove top and old burners to build into this idea). Off to another side will be the "island" so we can have an area to use for dry ice cooling if needed, a utility sink (hooked up to a hose) for washing vegetables and a small prep area. The tables and chairs are all rounded shapes. But you are right Token, everything else is very linear at our house. There will be slightly more flowing areas in the back: the dry creek will have some very gentle bends, there will be a round-ish dry pond, I bought an arbor with four sides that is rounded to put a hammock under. I think the cistern field will be a round shape too for simplicity. There are paths planned, they will be casual and not purposefully windy but gentle, not perfectly straight but close to it. Again, in my mind I had a rounded shape for a patio here but then I though that might not be conducive to having casual seating areas. There maybe be a small table, but it might be more of several chairs and side tables. We have another area close by with a rectangular table and 4 chairs on a retangular patio coming as well, but you won't be able to see that from the deck patio.

I have the same size main sink as you (12 inches deep though) and went with a round sink for the prep sink. I ordered a 16" round sink and it was frankly too big, but it sounds like you have plenty of room. I went instead with a 12" sink (round) and love the softness of the form in comparison to the main sink. It's a bit more interesting than two sinks the same shape. I think it will look great in your kitchen :) I don't think they really take up a larger cabinet than anything else. One think I like about the sink in the prep area is that I can sit the faucet at about 2 o'clock, verses directly behind it at 12. It uses the space well, and looks nice.

I love round tables. IMHO, a round table must go in a square room (which yours essentially is). Most DR are not square, so round tables are less common. I would totally do a round 72" for 8-10. With leaves if you have more. ETA - re the above ... do you have other eating areas? I would not use a formal DR for dinner for 3 anyway.

I have a small apartment which requires rugs (condo rules), and I have a rectangular rug in my living/tv space, circular rug in my desk/office area a couple feet away, then another rectangular rug in my dining space. I like that the circular rug sort of breaks up the two major areas (living and dining). I also have both rectangular art and circular mirrors/hats up on my walls, so I like playing with shapes. Per your photos above, I think that the rectangular and circular rugs would look great! What size rugs are in the pictures above? I hope this helps!