Legal Question in Business Law in California

Indeed, the law would prefer that contracts NOT outline penalties and forfeitures. Penalties and forfeitures are properly the province of a court of law, not the contracting parties. Sure, many contracts do provide penalties for breach, but courts may not enforce them, and if they do, it is because they are more in the nature of a reasonable pre-estimate of damages rather than true penalties or forfeitures.

In your case, you readily admit breaching the contract by departing without giving two weeks' prior notice. Under the circumstances, you are liable for the boarding establishment's actual loss of income, up to two weeks worth, but it has a 'duty' to make reasonable efforts to hold those losses to a minimum by trying to re-rent the space to another boarder, or by equivalent means.

I recommend trying to keep this out of Small Claims Court and negotiating a realistic but small cash settlement, such as you pay them for one week, but you get your tack back.