In my old house, I had a large bathroom and was able to hide my cat's litter box under a large counter top beneath the sink. In my new house, the bathroom is too small, so I had to move the cat box to the laundry room. Unfortunately, the laundry room is also small, and adjoins the kitchen with a door that remains open nearly all of the time. After a couple weeks, I was already unhappy with the sight and smell of the cat box near the kitchen and decided to improve the situation.
Nasty cat box right near where I cook food. This will not do, but my new house is very small, and I didn't have a good place to put the cat box. The solution was to cut a hole in the laundry room wall, and setup the cat box in the utility closet, which is normally accessible only from outside the house.
The bricks on the right make up the backside of the fireplace, and the white cylinder on the left is the water heater. I built a shelf that sits on part of the fireplace bricks and is also supported by the wall. The cat box fits perfectly into this space on the shelf.
The utility closet is open to the crawl space under the house and also contains the furnace, water heater, and other things that I would rather the cat not know about. I got some plastic lattice from Home Depot and built a small enclosure around the cat box shelf. The Depot also sells plastic track that accepts the edge of the lattice panels. I used some hooks to make the panels easy to remove. I will have to remove the panels to clean the cat box.
The cat door is a Petsafe Delux 4-way cat flap ($13). It was intended to be installed only in doors -- not walls and hence was not deep enough to extend through the whole wall. I used some 1/16" ABS plastic sheet, permanent double-stick tape and duct tape to make a tunnel through the wall.
After a few hours, I already notice the air smelling better in the kitchen and I was able to convince the cat to walk through the door on his own accord. It seems this project is a big success!