Bring cranberries, sugar, and water to a simmer in a 3- to 3 1/2-quart saucepan, then simmer, uncovered, stirring occasionally, until berries just begin to pop, about 2 minutes. Drain cranberries in a fine-mesh sieve set over a 1-quart glass measuring cup, then reserve 2 cups cranberries and force remaining berries through sieve into syrup. Discard solids remaining in sieve, then add reserved cranberries to syrup. Cool to room temperature. Transfer to a pitcher and chill until cold, about 2 hours.
Add remaining ingredients to syrup, stirring gently to combine. Serve drinks over ice in 8- to 10-ounce glasses.