Which possessions of Gulliver did the Lilliputians find? What is the capital of Lilliput?

The capital city of Lilliput is Milendo.

The Lilliputians find Gulliver's hat.

About two or three days before I was set at liberty, as I was entertaining the court with this kind of feat, there arrived an express to inform his majesty, that some of his subjects, riding near the place where I was first taken up, had seen a great black substance lying on the around, very oddly shaped, extending its edges round, as wide as his majesty’s bedchamber, and rising up in the middle as high as a man; that it was no living creature, as they at first apprehended, for it lay on the grass without motion; and some of them had walked round it several times; that, by mounting upon each other’s shoulders, they had got to the top, which was flat and even, and, stamping upon it, they found that it was hollow within; that they humbly conceived it might be something belonging to the man-mountain; and if his majesty pleased, they would undertake to bring it with only five horses. I presently knew what they meant, and was glad at heart to receive this intelligence. It seems, upon my first reaching the shore after our shipwreck, I was in such confusion, that before I came to the place where I went to sleep, my hat, which I had fastened with a string to my head while I was rowing, and had stuck on all the time I was swimming, fell off after I came to land; the string, as I conjecture, breaking by some accident, which I never observed, but thought my hat had been lost at sea.