Long term lease wanted: 1 bedroom in PA, MP, Atherton or RWC

I am seeking a 1-bedroom apartment or cottage in Palo Alto, Menlo Park, Atherton or Redwood City. I prefer to move in August but would consider July, September or October. Budget is around $3000/month.

Must have:
-Location within reasonable walking or biking distance to campus or to a Caltrain station
-Private outdoor space

Nice to have:
-in unit laundry
-dishwasher
-allow a cat (considering adopting)

I am a mature professional working full time in the Stanford Doerr School of Sustainability. My current lease is ending due to the owner selling the property. I have excellent local rental history and sterling references. Additionally, I am financially secure with a 800+ credit score and can sign a 1-year lease. I grew up in Palo Alto and am back in the area for work and to help take care of my elderly dad.

Please reach out if you know of a place that might work! Thanks for your consideration.
-Celia