"where he keeps" is correct and usable in written English.
You can use it when referring to a location where someone stores something. For example, "I'm not sure where he keeps his tools."
I know where he keeps his money.
"I know where he keeps his stamps", he told me.
As for where he keeps his Oscar, he said: "I keep it in a safe.
That is where he keeps his organ meat and deer ribs.
Mr. Pelham asks Harold to drive him to a trailer where he keeps his dog, Melba.
We're sitting in his office (that is, the place where he keeps lots of vinyl), either side of a desk.
Now they are back in his house in France, where he keeps them in a bathroom, safe from theft.
"He's one of those players where he keeps working, and keeps trying to improve as a young player".
Sometimes he partakes of a little laughing gas too, in the doctor's surgery where he keeps a small office.
Mr. Lightbourne spends winters caddying in Bermuda, where he keeps a family home.
Where he keeps his Oscar: I won it for "Nemo," for best animated picture.
