So he was definitely at the Burrow, and I imagine he stayed there. He would be able to take care of himself mostly, hunting mice and gnomes, and Mrs Weasley would take care of him, too. Since he's part Kneazle, I'm not sure that Hermione's parents would be great to look after him, and he definitely didn't go to Australia with them, so...
“I’m doing it, I’m doing — ! Oh, it’s you,” said Ron in relief, as
Harry entered the room. Ron lay back down on the bed, which he
had evidently just vacated. The room was just as messy as it had
been all week; the only change was that Hermione was now sitting
in the far corner, her fluffy ginger cat, Crookshanks, at her feet,
sorting books, some of which Harry recognized as his own, into
two enormous piles.