Hi marthas harbour and welcome to Cruise-chat. We stay at the TropiRock in Ft. Lauderdale. They have rooms with kitchenettes and usually rent by the week. It's located 2 blocks from the beach, it is an older motel, but in good condition and very clean. You can check it out
here, they may be able to accomodate you. Like Sandy said, it's hard to find someone that will rent for less than 4 nights, especially in the winter. Best wishes and have a wonderful cruise!