Add the sugar, 1 cup water and berries to a medium saucepan and bring to a simmer. Stir until the sugar has dissolved and press against the berries with the back of the wooden spoon so their juices leach into the mixture. Let sit and steep until cool.
In a large pitcher, combine the cooled raspberry simple syrup, lime juice and club soda. Pour into tall glasses filled with ice and garnish with a slice of lime and a few extra berries for garnish.