Place tea bags in a quart-size glass measure or heatproof bowl.
In a saucepan bring water just to a boil and pour over tea bags. Steep tea 5 minutes and strain through a sieve into a heatproof pitcher. Cool tea and chill, covered, until cold, about 1 hour.
Stir in nectar and syrup. Serve tea over ice in tall glasses and garnish with peach slices and basil sprigs.
To make simple syrup: In a saucepan bring sugar and water to a boil, stirring, and boil until sugar is completely dissolved. Let syrup cool and chill, covered. Syrup may be made 2 weeks ahead and chilled, covered.