Cover these 3 cities, how to plan start from which city? (Xian,Luoyang and Shanghai)which season for

As popular tourist cities in China, their transportations among the three cities are very convenient, either by flight or by high speed train. And it is closer between Xi'an and Luoyang. So I suggest you may travel Xi'an and Luoyang together and then visit Shanghai, or from Shanghai to Xi'an and Luoyang.

The most famous flower in Luoyang is peony, and the flowering period is from April to early May. I kindly suggest you visit some garden to appreciate the gorgeous flower in Luoyang at that time.