Stir sugar and 1 cup water in heavy medium saucepan over high heat until sugar dissolves and syrup comes to boil. Add cranberries; return mixture to boil. Reduce heat to medium; simmer until cranberries burst and sauce thickens slightly, about 10 minutes. Remove from heat. Mix in ginger; let stand 5 minutes. Mix in peaches. Cool. Chill at least 2 hours and up to 3 days.