In a small sauce pan, heat the sugar with 3/4 cup of water until boiling. Stir until the sugar dissolves, then remove from heat, toss in the basil leaves, and cover. Steep for 10 minutes. Discard the basil and let the syrup cool.
Roughly peel and slice 4 of the peaches. Add to a food processor and puree until smooth. This should make roughly 1 cup of peach puree. If needed, peel an additional peach or two and whip again in the food processor.
In a large pitcher, stir together the water, lemon juice, peach puree, and 1/2 cup of basil syrup. Taste and add more syrup as needed; you might have some left over. Cover and refrigerate for at least an hour until chilled. Stir and taste again to see if any more basil syrup is necessary.
Add a few peach slices to each glass and pour in the lemonade. Drop in a few ice cubes if you'd like, and garnish with fresh basil.
Notes
*Make it boozy: If you want to make the whole batch spiked, add 1 cup of your favorite liquor. I love either bourbon or rum in this! If spiking individual glasses, add 1-1.5 oz of liquor.