To make simple syrup: In a small heavy-bottom pot, combine water and sugar. Bring to a boil over medium heat. Once sugar is completely dissolved, remove from heat. Add basil to the syrup and let steep for at least 30 minutes. Remove leaves after 30 minutes and continue to let cool.
To make the cocktail: Juice your limes either by hand or with a juicer. Set aside.
Set a fine mesh sieve over a glass bowl. Set aside.
Remove the rind from the watermelon and cut the melon into large chunks. Add a couple of cups of watermelon to your blender and liquefy until no chunks remain. Strain purée through sieve. Repeat until all of your watermelon has been puréed (makes about 6 cups).
In a large, glass pitcher, combine watermelon purée, simple syrup and lime juice. Refrigerate until cold, about 2 hours. When ready to serve, fill a glass with ice. Pour watermelon 3/4 of the way up the glass. For the kiddies, fill glass with seltzer water. For the grown-ups, top off the glass with about 3 tablespoons chilled vodka. Garnish with lime wedges or fresh basil and a straw.