Great question! There are several local hangouts, some seasonal depending on crowds, and some pretty much year round or depending on live music . Some restaurants/bars close during winter for a month or so.... But here are a few real local places locals love...
Nicks in the Beach
Pandora's in Grayton Beach
Marie's Bistro in Blue Mountain Beach
Fire at Gulf Place
Hurricanes oyster bar in Grayton Beach
The red bar
Stinky's
Shorty's Surfside in Grayton Beach
Mctighes
I don't know if locals hang out there, but we really enjoy the happy hour at Calyza Pool at Alys Beach because they have a really good fried seafood appetizer that we eat as a light meal (and they're within walking distance from our place). We always enjoy going to Shades for their sandwiches (really good burgers and po' boys) - hearty food.