Welcome to the left coast. I have a son who lives in Williamsburg and the rents in Palo Alto seem to be equivalent to Williamsburg. When are you moving out here? I have a one bedroom in a 4 plex I manage that allows dogs that will be available in June. There is also a complex in Palo Alto called Southwood that allows dogs and is adjacent to a park that has a dog run. There is an apartment building in Mountain View called Avalon that allows dogs. You would probably enjoy being close to University Ave or California Ave in Palo Alto, Castro Street in Mountain View, or Santa Cruz Ave in Menlo Park. These are all close to Stanford and as close to city life as possible in the endless burbs of California.
If you want to walk to downtown the following communities offer that for you
Willow Glenn (San Jose)
Downtown San Jose
To seach for homes for sale my website has a spam free search. Also for rentals you can go to http://www.finestexpert.com/
Welcome to beautiful California.
I am a lifelong Peninsula resident except for 10 years living in Queens NY. Pls go to my website to search for property which will give you some idea of market values in Palo Alto area.