This rather more than a "shopping answer", hopefully.
How to determine if Jade is genuine:
This webpage provides an excellent discussion of types of genuine jade and of non genuine alternatives.
This page is also very useful
Excellent characteristics table for Jade and other materials.
A pocket spectrometer is possibly a really good tool. These are actually available at sensible prices - but few people would carry one :-).
Suitable lights will also show certain characteristics - see table.
Archimedes was here:
About the most useful test you can do "reasonably easily" is to measure density.
It helps to be a little cheeky and prepared to stand out from the crowd :-).
If you prepare for it this can be done very quickly and very easily at any location.
You need a suspension scales* or spring balance that can weigh a suspended item and a container of water large enough to suspend it in while weighing. Engineers and other people of similar bent will have no problem carrying the required equipment in a pocket. Willingness to use it or to ask permission to do so will depend on you :-).
*If you do not have a suspension scale / spring balance you can use the widely available low cost digital platform or pan scales as suspension scales by holding the scales "in the air" and placing a light stick (bamboo skewer or chopstick will work) across the pan and tying a thread from each end down to a point below the scales in a "V" and suspending the target object from there. This can all go in a pocket or bag.
Essentially you weigh the item suspend "in air" and then again while it is suspended in water. You use the weight in air and the weight change from in_air to _in water to measure density. (The weight change is equal to the mass of water displaced and is equal in grams to the volume in CCs (cubic centimetres) and density = mass / volume.
- **Density = in_air_weight in grams / (weight_change) in grams **
See the pages above, but genuine Jades will be about 3 to 3.3 for Nephrite and 32. to 3.3 for Jadeite. 2.9 to 3.0 is "maybe". Below 2.9 is not Jade.
There are many places to buy Jade and various "factories". One of the many which you will have trouble avoiding in certain circumstances is the one at Long Di - en route to the Great Wall at Badaling. Many tour operators include it in their trip to Badaling - either as an announced part of the tour or "unexpectedly" along the way. It seems to be about as good as any and you can judge the realness for yourself. This You tube video (not mine) shows a trip through their show rooms and some views of their craftsmen at work. It includes a brief comment on testing Jade for realness and of comparing it to glass and shows their show cases which have samples of Jadeite materials from many locations. Opinion only - if you have any ability at all to distinguish "realness" then a place like this gives you maximum chance - you can see the raw material, can see the objects being made and by their spiel they indicate that they are moderately open to people "testing" for realness.
I visited there with a tour group in (I think) 2008 as part of a Badaling day trip. The Jade factory was on the agenda. They told us that it is the only official state jade factory. It's not state and it's not the only one, so that's a guide as to how much you may be able to trust your guides :-).
NB: I bought a chunk of "Jade" from the Long Di factory cutting room rock pile. The price was good. Subsequent density tests show that it is NOT Jade, or is a mixed Jade and other material rock. So, even at Long Di, take care.
Excellent user discussion on Badaling and Jade factory and more