Make the simple syrup: In a small saucepan, stir together the sugar, 2 cups water, the celery, and celery seeds and bring to a boil over high heat. Reduce the heat and simmer for 5 minutes. Remove from the heat, mash the celery a bit with a wooden spoon, and let steep until cool. Strain into a jar or container with a lid and refrigerate until use.
To serve, fill each glass with ice, a couple of lime wheels, 2 ounces gin, 1 ounce celery syrup, and a squeeze of lime juice. Stir, top with club soda and a celery stalk, and serve.