Since you have been gone, we have moved twice.
The first time was in early 2008, from the Washington, DC area to southern Virginia near Yorktown, and the second time was in June 2009 from there to upstate New York, near the Canadian border.
We made the first move with our GSD Abby and our two cats, and the second move with Abby, our Malinois Ronja, and two cats. We got Ronja in March, so very shortly before moving, but did get her CGC and TDI prior to our move.
The way we found both those places - both are houses - has been through Craig's List, but not by contacting people through their ads. What I did was to post a "Housing Wanted" ad on Craig's List for the area we were moving to, explaining what we were looking for and giving some information about ourselves and our pets. I did make sure to include that both the dogs have their CGC and TDI, and also that we are carrying renter's insurance which does cover the dogs under its liability clause.
The place we lived in near Yorktown was half of a duplex and the landlord's daughter and son-in-law lived in the other half. We shared a yard (unfenced) and never had any issues. We were also walking-distance from a beach where I could take the dogs swimming, training, etc.
Where we are now, we have a split-level modern log home with 74 acres behind it, as well as another 100+ acres across the street (which belongs to our neighbor) that we are allowed to go on with the dogs to hike, train, etc. It's a really nice place to live and we're seriously considering buying it if DH ends up retiring up here.