Cape of Good Hope (the peninsula on the southwest tip of the deserted Centra continent), near a lighthouse.
Truth [Final Fantasy VIII Original Soundtrack: Disc 4, Track 03]
This orphanage was an idea of Sorceress Edea before she ever came up with the concepts of Gardens or SeeD; however, the goal was already pretty much the same: to offer orphans of the Sorceress War a place to spend their childhood and be loved. Squall, Quistis, Zell, Irvine, Seifer, Ellone and, of course, Selphie were all taken in by the kind Edea when they were still rather young (around the age of four for most of them). At a certain point, Ellone was sent to the White SeeD – "Edea's SeeD", which she trained herself – ship for her own protection; deprived of his "Sis" and desperate, Squall left in search for her. Worried, Edea went after him, only to find a dying Ultimecia in need of someone to pass on her powers to. Afraid that she might get hold of one of the children instead, Edea willingly took Ultimecia's powers, leading to what is called the "Final Fantasy VIII time paradox" (which I definitely won't be going into).
As time passed, the orphanage slowly emptied up, with Quistis and Zell being adopted and the remaining children sent to different Gardens, which had been created in the meantime. From this point on, we can not be sure what became of the cozy stone house by the beach; however, it is assumed that Edea stayed there until, years later (shortly before the start of Final Fantasy VIII), Ultimecia finally possessed her, leading to all subsequent game events. Either way, speculation aside, in the current time the orphanage is in ruins, although Edea still goes back to living there after Ultimecia leaves her body by the end of Disc 2.
Selphie spent her early childhood in the orphanage under the care of the beloved Matron; this is where she made her first friends, among which Irvine seemed to like her best. During the flashback scene at Trabia Garden, he describes her as "spunky little Sefie", which still seems rather fitting: indeed, most of the children's behavior back then is reminiscent of their present selves – except for Irvine, however, none of them acknowledge this, since contact with GFs deprived them of all their early memories.
Telling from the flashbacks, the children were quite happy at the orphanage; some of them, like Selphie (who else, right?), even managed to have fun from dawn to dusk, despite the tragic situation they were in. Edea was a wonderful Matron and Cape of Good Hope was a (accurately titled) lovely, comfortable place – even though Selphie was sent to Trabia Garden and eventually forgot all about her childhood, she speaks warmly of it once she gains her memories back. Also, she often says in her diary that Matron means a lot to her, and states how difficult it is for her to be faced with the need to fight her, Edea being the woman who took her in and offered her a chance at life.