Stanford Hospital Employee Seeking Housing

Hello! I am a Stanford Hospital employee urgently looking for housing as my current rental has a piping issue necessitating construction and causing me to need to vacate early. I am looking for a 1B/1B (or larger) for under $3,500 per month in Palo Alto or Menlo Park ideally. I am looking to be a single occupant (no shared housing), and have one cat. Please reach out with any leads!