Hi, could you recommend the best way to visit wineries in the Shandong area if I was traveling down from Beijing?

Hi, the wineries are very common in this province. Generally, there are several in severy city or area. Here are some good ones I know:
Jingzhi Liquor Company at No.010, Jingjiu Main Street, Jingzhi Town, Anqiu City (it has a website with Chinese and English version);
China Jingyang Ridge Alcohol at No. 17, Zishi Street, Yanggu County;
Bandaojing Winery at No. 55, Central Roadm Gaoqing County, Zibo City.
Besides these above, there are more. I suggest you turn to a local tour guide who is very experienced with the Winery Travel to cover some good ones.