A New Canaan woman who recently moved to town has opened a children’s games, toys, clothing and accessories shop on South Avenue, in the space known to generations of locals as the Sweet Shoppe. Amanda Cui said she visited New Canaan in November on a friend’s recommendation and moved to town earlier this month with her family, including her 2- and 7-year-old daughters. “I saw the stores and the neighborhoods and I liked it,” Cui said on a recent afternoon, standing between two kids’ stations—one for creating model ice cream sundaes, another for lip gloss—at the front of her colorful, eclectic shop. Funky Monkey opened Friday. “I saw that they don’t have this stuff.