You may want to contact a real estate agent and ask for help with the process. In general, the landlords will not pay realtors anymore (because of craigslist), so you typically will have to hire the realtor yourself. The standard is 3 percent of the rent for a year. You could argue 3 percent of six months since that's your intended occupancy!
I worked with my former broker to find he and his wife a rental home when he moved here to Palo Alto from Chicago about two years ago. One thing I noticed was that the rentals that seem to be the very best deals may be in the less desirable neighborhoods bordering on East Palo Alto and East Menlo Park. Near downtown Palo Alto, there are corridors that are amazing and beautiful -- and some that you may want to avoid.
Other realtors will help you for no charge, for the "promise of someday" helping you buy your next home.
I grew up in Palo Alto and would be happy to help. It's a little skimpy finding rentals right now and we'll see things open up in June when Stanford gets out and people make end-of-year moves. There are a few condo conversion projects that provide good short term rental opportunities as they are not seeking long-term occupants.
If you have any contacts at Stanford, there are excellent rental boards within the university community but many exclusively provide rentals to staff and students of the university.
Erica M Nelson