There's only one city where the people'accent most similar to the standard Mandarin, it's Harbin(哈尔滨), of course in Northeast China! The most northeast of China! But other places of Northeast China all have strange accents.

Bejing is the best standard

I think, it depends on what you want. As far as I know, the whole NorthEast of China speaks a variant of Mandarin in daily life. If besides chinese lessons, you want to communicate with people during your stay, the best region for learning nice Mandarin would certainly be the big NorthEast. Of course, Beijing dialect is the origin of Mandarin, but Beijing people have an accent: they use a lot of rr. That is not standard Mandarin. Some non Beijing people sometimes associate the abundant use of rr with arrogance. I have twice followed summer courses in Beijing. The teachers in Beijing that I have met dont use the anundant rr, and speak a beautiful standard Mandarin. For me, the rr from common Beijingnese people is rather disturbing and makes comprehension for me sometimes difficult or slow. As my level advances, hopefully accents will disturb less and less. If you just want to focus on good lessons with good Mandarin speaking teachers, you can find good ones in whole China, but you need to select a good university or a good institute. I have heard that lessons are not always automatically good quality. It would be safe to have references. I am learning Chinese for about three years, and have passed two times in Beijing learning Chinese. That was a real pleasure. Both the good lessons and the nice cultural sites and atmosphere in Beijing. I am now thinking to go to a city in the NorthEast, but not Beijing, cities like Tianjin, Jinan, Qingdao, Dalian.

beijing or shanxi(山西)

Not really actually.some said the Henan provinve will be the best.But actually is not.I think Hunan or Hubei is better.