For 2 adults and 2 children, is it better to stay on Shamian Island or at Guangzhou downtown?

Well, if you want to explore the European-style buildings and relax yourself, you may live on the island. If you want to travel around the city, living in the city proper will be a better choice. :) Personally, I recommend you stay in downtown area for easier access of trransportation, dining, shopping and sightseeing.