This is what I was thinking. In city areas, unless you are really, really willing to go through a pet services site, you are going to have a hard time finding a place to rent with a dog.
We're lucky. Like I said, we rent, but we have the sort of place where dogs are welcome and comfortable, as we have a huge yard and a lot of "open" space in the unit itself. (it's not a complex, it's a friend's father's multi family home and he adores dogs). Before we got a dog, we did some research on where we could and could not rent with him in case we need to rent elsewhere before we buy.
We found that in urban areas, it was very hard to find a place, in suburban areas it's not as bad w/ multi family homes. In complexes it's almost impossible. And many of the places that do allow dogs will charge a security fee for that to cover their homeowners.
So, really, if you are planning on renting in the city, in a complex you are severely limiting your cheap rental choices by keeping the dog, who, please don't take this the wrong way, but I can't see how you afford to feed him and take care of him anyway.
I am willing to help if this is something you want to do.