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Rabbits can be raised in a small space - garage, balcony, in the house, or in a back yard. Generally, they'll need a cage or hutch, they tend to dig their way out of a yard if not confined, or they go underground and you cannot find them.
If you need a meat animal, and have very little space, they are ideal, because they produce a lot of meat in limited quarters, and they are very efficient at converting feed to meat.
Raising rabbits for fur or fiber also takes very little space, compared to other fiber animals. Angora rabbits can be raised as pets in the house.
They do create some smell - this can be managed through weekly changes of bedding, or by use of vermiculture under the cages if you use a drop style waste management under wire bottomed cages.
In very limited space, rabbit cages can be stacked three high, in racks, with drop pans under each cage. This kind of system is available through several retailers online. This will work in a garage, where the smell is not as important an issue as it might be indoors.
If you are raising them in the house, you might wish to use plastic bottomed cages with bedding in them. This contains the mess and odor more. You can build a simple rack to place the cages on if you need to stack them. We use these for our chick brooders, a rack is easy to build to hold them (instructions in the Cages/Hutches article).