I would probably try to go with La Jolla/Bird Rock or even Pacific Beach. Will you be able to take a bus? If so I'd try to locate not too far from Route 30.

I like the little neighborhood south of La Jolla, called "Beach Barber" or "Windansea", there are some small cottages there although not sure how much luck you'll have with a one month rental. Try VRBO.

There is a Vons in La Jolla at Pearl and Fay.