Seeking 1BR or studio near Stanford or Caltrain for short- or long-term lease

My husband and I just moved to the area to teach at Stanford and we are looking for housing.

We are looking for:

• A 1BR or studio apartment or ADU
• A full kitchen, including a dishwasher
• Ideally either a shorter drive to the Palo Alto campus or walking distance to any Caltrain station

We're happy with long-term unfurnished leases or short-term furnished ones.

We're hoping to keep the budget as close to $3000/month as possible, but can be a bit flexible for the right place.

Any and all leads welcome and appreciated!