We are renting here in Colorado. I sold my house in NJ without even being able to see what I was moving into (Rob did it all before Bojie and I got out here). I didn't want to commit to buying until I lived out here for a while and got to know the towns and communities. Actually there are several Newf owners out here who rent. We emphasized that Bojie is CGC and a therapy dog. We also educated them on the breed, that he is not the type of dog who runs laps outside in the yard all day barking, etc. Rob also had 2 cats. When we got Rigsby, we asked our landlords permission first and they said yes without hesitation. Our biggest issue here is the flooring. I've covered the hardwood with foam interlocking tiles, the off white carpet in some parts of the house doesn't really stand too much of a chance...more because of my husbands messiness than the dogs.
I think it really depends on what area of the country you are moving to. CO is SO pet friendly it is difficult not to find pet friendly property including townhomes, condos and apts and single family homes. But wherever you go, they are there and available, just more in some areas than others. Craigslist is a good place to start, and online realtors as well.