The hotel just called, stating that it has increased the rate and will not honor the rate quoted. The hotel says I am free to cancel, but unfortunately, canceling is not an option at this late date, since I can't find a replacement room in the area. If you have written proof of the rate, or you used your credit card, your chances of recourse are greater than if a clerk simply gave you a price quote over the phone. I've certainly heard of hotels setting rates, then deciding they have priced their rooms too low and increasing them.
Properties are free to charge whatever amount they can get away with . . .
But it is unethical for a hotel to renege on its promise to someone who has already made a booking. If it does renege, it should find you a comparable room at an alternate hotel and refund the price difference between your original rate and the rate you end up paying. If you guaranteed the rate with your credit card, seek help from your credit card issuer. There may be a rule in the contract between the hotel and your card issuer that will work in your favor. Furthermore, if you used an American Express card, the hotel is obligated to pay for the first night's stay.