Learn French: Le tapis est au milieu du salon. - The rug is in the middle of the living room.

In French, the fixed expression for "in the middle of" is au milieu de. Even though English says "in", French uses à (which combines with le to become au). You will almost always use au instead of dans with milieu.

Why does the sentence use du salon instead of de le salon?

In French, the preposition de (of) and the masculine article le (the) must always contract to form du. Since salon (living room) is masculine, "of the living room" translates to du salon.

Does tapis mean an area rug or a wall-to-wall carpet?

Le tapis usually refers to an area rug. If you want to talk about wall-to-wall carpeting, the French use a different word entirely: la moquette.

Can I use chez with this phrase to say "in the middle of my place"?

Yes, absolutely! Because chez moi acts like a noun meaning "my place", you can put it right after the preposition de. You would say au milieu de chez moi. Notice we just use de and not du, because there is no le in front of chez moi.