You might also ask “where should I not put the cat litter box?” And then go from there.
Would you like to eat and sleep next to your toilet? When you take a train you don’t head for the toilet area and find a seat there. Yet, it seems that quite a lot of cat owners line up the food bowl, the water bowl and the cat litter tray in a neat row. This is not a good idea. The litter tray should be accessible but away from food and water.
With that out of the way, where is the ideal spot for a cat litter tray? In the wild, the North African wild cat (the domestic cat’s ancestor) would probably defecate and urinate in prominent positions on the boundaries of his territory and at major junctions within his usual trails. This is because he is also marking his territory.
For humans, it is not suitable to put the cat litter tray in a prominent position within the household which is, in effect, the territory of a domestic cat; certainly if he is a full-time indoor cat.
Quite obviously, the cat litter tray should the out of the way but as a compromise, somewhere where it might be able to also double up as a scent marker. This might be, for example, somewhere near the back door which is a prominent boundary point where other cats have access to his/her world if there is a cat flap. As it happens, I don’t do that myself nowadays although I did at one time. My general philosophy is that the litter tray should be in a place which suits me but if I do that I’m not making any real concessions to my cat.
In addition the tray should be in a quiet area where the cat feels about to leave unhindered. There should be easy access and exit.
I would have thought that 90% of cat owners want to ensure that there are no smells from the litter box in their home. It is easy to generate a cat smell in the home which is not picked up by the owner because she has become acclimatised to it. There are inventive ways to remove cat litter smell from the home and there are commercial products made with this objective. One is the Katio which is placed against a window and has a vent to the outside and a cat flap for the cat to access it.
The bottom line is that it should be away from your cat’s food and water. Also, in my opinion, it would be wise not to move it once sited because once a cat gets used to the spot he gets used to the scent from that area and returns to it to go to the toilet.
These are, in general, my thoughts without reference to other sources. If you have a certain place in your home or even outside your home where you place your cat’s litter box, please tell me in a comment.