The phrase the eighth wonder of the world is used hyperbolically of any impressive object, etc.

This phrase refers to the seven wonders of the world, designating the seven most spectacular man-made structures of the ancient world, which traditionally comprise:
1-: The pyramids of Egypt, especially those at Giza;
2-: The Hanging Gardens of Babylon;
3-: The Mausoleum of Halicarnassus;
4-: The temple of Artemis at Ephesus in Asia Minor;
5-: The Colossus of Rhodes;
6-: The huge ivory and gold statue of Zeus at Olympia in the Peloponnese, made by Phidias circa 430 BC;
7-: The Pharos of Alexandria (or, in some lists, the walls of Babylon).

The phrase the eighth wonder of the world is also applied ironically to a self-satisfied or arrogant person. In fact, the earliest occurrence of the phrase that I have found is from the title of a satiric attack on the English traveller and travel writer Thomas Coryat (circa 1577-1617), by the English poet John Taylor (1578-1653), printed in London in 1613 by Nicholas Okes:

The eighth wonder of the world, or Coriats escape from his supposed drowning. With his safe arriuall and entertainment at the famous Citty of Constantinople; And also how hee was honourably Knighted with a sword of King Priams. With the manner of his proceeding in his peregrination through the Turkish Territories towards the antient memorable Citty of Ierusalem.

In the 17^th century, the eighth wonder of the world was especially applied to the Escorial, a monastery and palace in central Spain, near Madrid, built in the late 16^th century by Philip II (1527-1598), King of Spain from 1556 to 1598.

These are four 17^th-century occurrences of the eighth wonder of the world as applied to the Escorial:

1-: From The Darknes of Atheism Dispelled by the Light of Nature: A Physico-Theologicall Treatise (London: Printed by J. F. William Lee, 1652), by the English physician and natural philosopher Walter Charleton (1620-1707):

The breast or laboratory of a Bee contains more anfractuous convolutions then the Labyrinth of Dedalus, and more Cellules then the famous monastery of St. Lawrence, in Spain, for bravery and amplitude of architecture reputed the eighth wonder of the World.

2-: From Epistolæ Ho-elianæ: Familiar Letters, Domestic and Forren. Divided Into Sundry Sections, Partly Historicall, Politicall, Philosophicall. With a Fourth Vol. of New Letters Never Published Before (London: Printed for H. Moseley, 1655), by the Anglo-Welsh historian and political writer James Howell (circa 1594-1666):

I was yesterday at the Escurial to see the Monastery of Saint Laurence , the eighth wonder of the world , and truly considering the site of the place, the state of the thing, and the symmetry of the structure, with divers other rarities, it may be call’d so.

3-: From A New Survey of the Present State of Europe: Containing Remarks upon several Soveraign and Republican States. With Memoires Historical, Chronological, Topographical, Hydrographical, Political, &c. By Gidion Pontier, &c. Done into English by J.B. Doctor of Physick (London: Printed for W. Crooke, 1684):

The chief Houses of Pleasure belonging to the King, and out of Madrid, are
Il Campo, il Retiro, Aranjues, le Pardo, the Escurial, and Jarzuela.
The Spaniards make of this last save one the eighth Wonder of the World. Philip the Second laid out twenty Millions in building it: he caus’d the Escurial to be built both in memory of the Victory which he gain’d over the French, An. 1557. at S. Quentin in Picardy on the Somme, the tenth of August, being S. Laurence’s day, and for having caus’d the Church of S. Laurence of S. Quentin to be beaten down; whereupon he made a Promise to God to cause a finer to be built in Spain, in the honour of the same Saint, and a Monastery where the Monks of S. Hierome are magnificently seated.

4-: From The Revengeful Mistress: Being an Amorous Adventure of an English Gentleman in Spain (London: Printed for R. Wellington, 1696), by the English poet and translator Philip Ayres (1638-1712):

The other Palace is seven Leagues
from Madrid, which is about twenty
English Miles, and is that Celebrated
House, the Escurial, built by King
Philip the Second, at the foot of the
great Mountain which they call La
Sierra de Guadarama, and by him it
was Dedicated to St. Laurence the
Martyr, who had been broil’d to
death on a Gridiron. The Spaniards
term this Magnificent Pile the
Eighth Wonder of the World: And
well they may; for ’tis of so prodigious
a bulk, that it seems capacious
enough to lodge the Inhabitants of
a small City; and yet ’tis so very regular
and uniform in all its parts,
that there is not a Tower, Pinacle,
nor Window on one side, which has
not the same to answer it on the
other.

The phrase the eighth wonder of the world is applied to the Castle of Osaka, in Japan, in the following passage from Atlas Japannensis: Being Remarkable Addresses by Way of Embassy from the East-India Company of the United Provinces, to the Emperor of Japan. Containing a Description of their Several Territories, Cities, Temples, and Fortresses; their Religions, Laws, and Customs; their Prodigious Wealth, and Gorgeous Habits; the Nature of their Soil, Plants, Beasts, Hills, Rivers, and Fountains. With the Character of the Ancient and Modern Japanners (London: Printed by Thomas Johnson, 1670), by the Dutch author Arnoldus Montanus (circa 1625-1683), translated by John Gilby:

None hath bestowed more Cost and Charges towards the building of this Castle, making it the eighth wonder of the World, than the Emperor Taicosama, who falling sick in Fißima, troubled himself exceedingly for his young Son Fideri, his sole design being to settle him in the Throne, and make him Monarch of the Japan Empire.