House rabbits make wonderful pets.
Buying a rabbit to keep in an outdoor cage is both cruel to the rabbit and pointless for you.
All of the domesticated rabbits are European breeds. They are social animals. Read Watership Down sometimes. Although there is a lot of fantasy, Adams did base much of the rabbit behavior in his book on another book called The Private Life of the Rabbit, where the author reported on a five year observational study of a warren of rabbits in Wales. The results shattered many myths.
What will happen is that the rabbit will become boring and neurotic. It will spend most of its time just sitting in place chewing on whatever you give it. After about 6 months, you will start telling your friends, “Rabbits are so boring, I don’t know why anyone would ever get one as a pet. Just a waste of money.” It makes just as much sense as getting a dog and keeping him in the same cage all day.
The Bay Area also has a problem with myxomatosis, a disease spread by mosquitoes that takes down a lot of outdoor rabbits.
You may also read somewhere that 50 degrees is the ideal temperature for rabbits. This is a story started by farmers who are breeding rabbits for fur. A low temperature encourages a thicker coat. If you ask actual rabbits what the ideal temperature is, they have told me it is taking a nap on top of the living room heater duct or pressed up against the fireplace grate when a fire is going.
And there is the problem of animal attacks. Raccoons, birds of prey, and other animals will attack the outdoor cage. They will, at the very least, terrify the rabbit and they may very well find a way to get inside.
On the other hand, a house rabbit can make a wonderful pet. Yes, they can be litter box trained. (If you get one from a reputable rabbit rescue organization, they will almost always be already trained.) They will adapt to your habits and schedules, although you may find yourself adapting to theirs some, too. (Compromise!) They will be interesting, sometimes frustrating, and irresistibly cute. You will have to get used to living with a litter box or two, you will have to bunny-proof the house a bit, and learn to live with some teeth marks here and there.
Please consider bringing a rabbit into your home. Better yet, consider a bonded pair. But forget about keeping a rabbit out in the yard.