Most rentals cam be found on Trulia, Zillow, or Craigslist. Occasionally they are on MLS, but not often. You can also contact apartment complexes directly. For example, Avalon allows dogs, is in downtown MV, but has a weight limit. There is a lot of competition for rentals in Mountain View. so do not get discouraged or surprised by how difficult it is. You may want to see about staying at a Marriott Residence Inn where they allow pets in order to give yourself time to find a place to rent.
Keller Williams Realty Pal Alto