Here comes the "don't call yourself a chef" squad.
There are a lot of great food cities.
San Francisco CA
Los Angeles CA
New York, NY
It depends what you want and what you are looking for. Cities like Raleigh, Charleston, etc are smaller and probably less expensive to live in, while still maintaining a food identity and culture. Cities like New York and Chicago have world class restaurants that will propel you through your career.
Even in Arizona places like Scottsdale could be a great place to live and work. There are lots of great hotels, resorts and restaurants there.
There are great restaurants and chefs in every corner of the country...you might just have to seek them out. You should start with some research about cost of living, climate, culture, etc and whittle down where you want to live. Then get a plan together for a job. Visit the city if you can.