Service animals are animals that are individually trained to perform tasks for people with disabilities such as guiding people who are blind, alerting people who are deaf, pulling wheelchairs, alerting and protecting a person who is having a seizure, or performing other special tasks. Service animals are working animals, not pets. Under the Americans with Disabilities Act (ADA), businesses and organizations that serve the public must allow people with disabilities to bring their service animals into all areas of the facility where customers are normally allowed to go. This federal law applies to all businesses open to the public, including restaurants.
For non-service animals - i.e. pets - you will have to consult with your local municipal code. For example, the City of Belmont, WA specifically prohibits non-service animals in public restaurants. In fact, it requires that all dogs be on a leash except in designated dog exercise areas.
Interesting question considering many cities, even those close to each other, have different oridinances governing this. Service dogs are almost always excluded from any city ordinance prohibitions concerning this subject. With that in mind, I would conact your local city council member or mayor's office and inquire about your city's ordinance on this subject. Remember, each city is different and has different laws on this issue.
The answer will vary from municipality to municipality, county to county, and state to state. It could even be different based on whether the restaurant is inside the city limits or out in the unicorporated area of a county. It might even vary based on whether the restauyrant has outdoor seating with pets permit outdoors but not indoors.
The bottom line is that most locations in the United States prohibit all animals (other than service animals) from being inside any restaurant, grocery store, or other place that food is served or sold. You will have to check with your local authorities to determine what the law is in your particular location.