Could your piano work on the wall at the bottom of your plan by "open to foyer"? It wouldn't actually be in either room and you could use the larger room for your dining space. If you do that, what will you use the smaller space for?

The area labeled 15x13 is measured wall to wall, including the area open to the foyer. I could put a piano there (which could be pretty to see from the foyer). But that leaves me with about 9x13 ft to fit a table for 8. I think that may be crowded, but I'm open to the suggestion. What size table do I need for 8? Also, I'd be a bit concerned that if the table and the piano are immediately next to each other, somebody may be tempted to use the piano as a sideboard! Yikes!

I would probably use the 12x12 room for dining then - if you are okay with the china cabinet being on that long wall adjacent to the foyer, or in the other room, if the piano goes on that wall. Or the piano in the larger room with the china cabinet on the long wall. Looks like a 60" round table would work in the smaller room and could seat 6-8, if you are careful about chair scale. A 48" with leaves might work, too, if you normally seat 4-5 and just extend to 8 for parties/holidays.

60" table in 12 x12 room:
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It's going to be very tight, and the piano is a very big object to get into this small space.

If you want the dining room fixture to be aligned with the center of your windows, the china cabinet will have to be placed on the wall with the kitchen door.

With bevangel's arrangement, I'd rotate the dining table 90 degrees, otherwise you don't have enough space to get into and out of the chairs easily.

suero, not sure how rotating the table helps anything. Now there's less space to walk to the kitchen.

"suero, not sure how rotating the table helps anything. Now there's less space to walk to the kitchen."

But with the rotation two people are not trapped against the right wall when seated...

I think a 48 inch round with a 20 inch leaf will still only fit 6 people because of the oval shape. If you could do a 42 inch by 72 inch rectangular table, you can put 4 or 6 regular chairs there and add 4 card table chairs when you have 8. I've done that and it worked fine.
My daughter has that size table in her dining room (40 by 72). Her room is 13 by 13.
The china cabinet and table will fit best if you can center your chandelier over the table, but closer to the window. That will give you the recommended 3 feet for the chairs to be pulled out.
You could turn your table the other way with the buffet on the dining room wall viewed from the foyer. You will have less space between the table and china cabinet for the chairs, but you will have more room to walk thru the dining room to the living room.

I have a 12x12 dining room with a walkway to kitchen, similar to you. I considered a round table, but ultimately decided against it because if I used a leave, the table would be 60x84 (60 inch round table with 24 inch leave). I just thought that was unmanageable with a china cabinet. Instead, I purchased a trestle base table with smaller chairs than the fully upholstered ones I had previously.

The table will work best with the table positioned as Bev27 shows because there is walkway to each chair rather than people having to walk around the table to their chair.

When I am not entertaining, I put the arm chair that in the corner of the room instead of at the head of the table to give more room to the walkway for everyday use.

Revised table layout for dining room.

How would it look if you rotated the piano so the flat side was along the wall? I'm picturing walking into the space from the foyer and having that piano in the way. Maybe with the rounded narrower end facing the foyer it would be more graceful, and the piano top would open up into the room rather than into the wall...

Also, with the rectangular table, I think the buffet has to go on the long wall. Then there would be room for two DR chairs on either side with seating for 6 when the table is without a leaf.

The only other arrangement I could think of would be to put the piano in the corner in the LR and then arrange the rest of the space as if there were walls on both sides, but leaving a traffic pattern through to the DR.