There is a wardrobe next to the bed at the right.
While no grammatical errors are throwing themselves at me for that sentence, it doesn't sound right to me.
There is a wardrobe next to the bed on the right.
Sigh of relief. That makes sense.
There is a wardrobe next to the bed to the right.
That one makes sense.
There is a wardrobe next to the bed in the right.
That means something different. That is using a different meaning of "right". It means that the wardrobe is righteous in its cause. That doesn't really make sense. You might say that one army in a battle is "in the right."
The ngram comparison of the others shows that "on the right" is the winning phrase. "To the right" and "at the right" are pretty close to each other, but far below "on the right".