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!