$1150 Looking for a room in 2br/2ba in palo alto (palo alto)

I'm looking for a room in a 2br/2ba apartment (or a house with a room and private bath). If you're a working female professional/student - it would be ideal. I'm willing to pay up to 1200 but would prefer to pay 1000 or below. I do have a preference for living close to the Palo Alto downtown area where I can access coffee shops, etc.

As an option, if you have a 2br/2ba that you are scouting for and need a roommate (don't have a place yet), we can work on finding a place together. I would like to move before December if possible.

I don't have a dog and don't intend on getting one now but dogs very welcome.