The area is very square and straight edged, so I think a round table would soften up the space. If you do a 60" round pedestal table, you should be able to fit 7, maybe 8, chairs as long as they aren't very large. The pedestal should be simple to allow as much space to push the chairs in.

I have a 60" round, but I have large chairs so I have 6 chairs for daily use , but can just squeeze in a 7th. For more flexibility, you could do a 60" round with a leaf or two, for when you have a large group.

My dining room is 11' x11'. When I had my 58" round glass table in there, it was a little bit of a tight fit for the person pushing back from the table next to the wall (no buffet there at the time), but doable. I now have a oval table that is 42" wide, and have leaves to make it larger. With all the leaves in it, it seats 6 people comfortably. I do have a small buffet type of table (40"L x 15"deep) next to one of the walls where 2 people sit near, BUT, they have to be skinny people to push away from the table since the buffet is behind them. (In this case it is always my DD who is very slim). But at the ends of the table for the 11'x11' room there is ample room. In your case of having 15' at one end you should be fine IMO.

On my blog link, in the first picture you can see how the oval table works in my room, in this shot it only has 1 leaf in it, but as I mentioned 2 leaves are fine in there too. Also, the photograph is deceiving in how close the buffet appears (due to the angle I took the pic) next to the table, there is still enough room for my DD to push away from the table. I suppose ideally, in my case, the buffet would be best removed, but her and SO's visits are only occasional.

Here is a link that might be useful: DR