If a dog is found abandoned does it have to go to the Shelter in the city it is found in? Can I recommend bringing the dog here?

If someone brings us a stray animal and we have space to take it in, we generally check it in as a remote impound at the city shelter where it was found. Checking an animal into the city shelter is the best way to get the animal back home

You should bring it to the city that the animal was found in. That way the owners can find them. They are going to look at the city shelter first before they look at a non profit like this.