The short answer is that there isn't any reliable place to buy jade, and if you buy you will almost certainly be sold something else. In passing, China's interest in jade isn't an indication that the country ever had much of either of the two (green) jade stones--jadeite and nephrite--which it used to import from around Khotan (now in Xinjiang) which hasn't had any decent sized pieces for more than a century, and in greater volumes from Indo-China. These days the Chinese import from sources such as British Columbia and New Zealand, so even if you find some jade, unless antique (which brings export problems), it will likely anyway be of kinds obtainable more cheaply elsewhere.

In general nothing with an internationally recognized tradeable value can be found more cheaply in China, and for items such as jewellery and precious and semi-precious materials which can be faked for a fraction of the cost of obtaining the real thing, these will indeed be faked almost 100% of the time. This is especially true when the target market is those unused to buying such items and so with little or no experience of detecting fakes, with no real idea of prices, and with deep pockets. And you, dear visible foreigner, are assumed to be prime target market.

Confine your purchases in China to the simple, pleasing, and inexpensive, and also avoid 'antiques', carpets, pearls, and so on unless you are very well acquainted with these things (in which case you'll be very unlikely to buy anything anyway).

If you really must shop for such things, first visit shops selling jade items in your own country, talk to sales people, ask about authenticity issues, pick up and heft the items for yourself, and make detailed notes of prices. It will still be hard to compare like with like, but without doing your homework thoroughly you'll be simply a lamb to the slaughter.

Peter N-H