In a medium saucepan, combine the water and sugar and bring to a boil, stirring with a wooden spoon until the sugar dissolves. Reduce the heat to moderate and simmer for 5 minutes; let the syrup cool.
In a blender or food processor, combine the sugar syrup with the basil, cilantro, mint, tarragon, lemon zest and lemon juice, and puree. Let stand for 1 hour, then strain through a coarse sieve, pressing on the solids with the back of a spoon to extract as much liquid as possible.
For each drink, pour Â¼ cup of the fresh herb syrup over cracked ice and fill with club soda. Garnish the drinks with a lemon twist, mint sprigs, and serve.
To make a cocktail, add half a shot of vodka and half a shot of rum to each drink.