Bring sugar and 1 1/4 cups water to a boil in a small saucepan, stirring until sugar is dissolved, 3 minutes. Remove from heat; let cool 15 minutes. Syrup can be refrigerated for up to 1 month.
Combine lemon juice, fruit, and basil in a bowl. Add syrup; mash lightly to release juices. Refrigerate at least 1 day and up to 4 days.
Combine fruit mixture and vodka in a pitcher or punch bowl; ladle about 1/3 cup into each glass. Fill with ice. Top with sparkling water, garnish with more basil, and serve.