The best place to adopt a dog is at your local city or county shelter or a nonprofit rescue group. Most government related shelters have information about their policies and adoption process, which are publically posted on city and county websites.
Shelters usually have a wide variety of dog breeds available including a large population of mixed breed and senior dogs. Sadly mutts and older dogs are often over looked by perspective owners and in dire need of a home. And, they can be the most loving and grateful dogs to own.
Nonprofit rescue dog groups care for older and mixed breed dogs as well, but some groups specialized in particular breeds who are most at risk due to puppy mills, dog racing, and owner misuse. See the links below for links to rescue groups who specialize in saving and rehoming these most vulnerable dog categories.