Moving to STT..need a place to live!

My husband and I are moving in about a week or two and we need a place on the east side of the island near or about Red Hook. It's just the two of us and a small cat. We don't have much in the way of deposit money yet, he's got a job and we need to wait for a paycheck to come in. We need a temporary place that will allow a small cat. Any suggestions will be greatly appreciated!