@veravdn: "employer applies for the work permit, which I will then take to the consulate to get my visa"

Still not right.

First the employer applies for "work permit notice", which you take to consulate to get a work visa.

The work visa allows you get get in the country, after which your employer will have to separately apply for the final "work permit".

"work permit notice" could be described as a document addressed to consulate, saying this:

"yes, we will give this foreigner legal employment in China, just give her the visa so she can get here".

While the final "work permit" could say:

"you are now employed in company X, ranked as class A/B/C foreigner"

Getting off-topic, but while there let's keep going.

Some cities allow foreigners (who are already legally in country with another type of residence permit), to apply for work visa and work-based residence permit without leaving the country at all.

If I recall correctly, the online electronic system where work permit/notice applications are inputted, contained this option in the menu. But Kunming authorities either didn't know how, or were not allowed, to have us use it.

I was already legally in China on marriage-based RP, but we were going back home for couple of months anyway, so we didn't challenge them for that option and applied for visa while away.

My experience in Chiang Mai was a little over two years ago.

Maybe the system has changed, but I thought that the consulate at which you apply is specified on the invitation letter by authorities in Kunming (based on your request) and that consulate must process your visa.

For example, when I did it in Hanoi many years ago, the Hanoi embassy was not accepting tourist visa applications from non-Vietnamese. And, while they didn't seem thrilled to see me, they nevertheless duly processed my Z visa because I had an invitation letter specifying that I apply at the Hanoi embassy.

Again, my info us out of date, and I know there have been a lot of changes in the past few years.

Dan's experience is valid still (as of August 2018), and that "invitation letter" is called "work permit notice".

I had not applied for work permit in the past, so I don't know how the invitation letter looked like before. But now it is a standard printout of the data that your employer has inputted about you and the employment to the online system, accompanied by the company stamp.

It includes a barcode, that consulates and other authorities can scan to quickly access the whole data in the electronic system.

We just went a couple weeks ago to Chiangmai to switch from a tourist visa to a work visa. Because we had all the correct paperwork (invitation letter, bar code, etc), it went smoothly. However they said we could not select the express service since we were not Thai citizens. We had to wait about 6 business days to get it back.

Having to travel to another country for a visa is one of the absurdities of living abroad.

I'm unsure of any advantages of going to Chiangmai over Bangkok or Hong Kong. The ladders both offer express service and are cheaper in airfare by quite a bit. I went to Bangkok twice and Hong Kong once for this process and had my work visa finished the next business day in the afternoon. By night time I was back on a reasonably priced flight (booked after I picked up my visa) to Kunming without any further trouble. The only other complaint I might have is that Americans have to pay through the nose for the visa and express serviced compared to any other country. If you are trying for a nice holiday and are not in a hurry then, by all means, book a flight to Chiangmai. Otherwise, the low cost of expenses is negligible considering you need to spend an extra 5-6 business days for processing.

Chiangmai Consulate - attitude. Some years ago I was there to get a visa after having inadverdantly overstayed a previous student visa. I was a little worried and figured I should, um, be pleasant and apologetic, so spoke to the pleasant, attractive young woman behind the glass window in Chinese, which was appreciated. Short chat over my visa, which I got - she noticed my several previous Chinese visas in my passport and asked why didn't I get a longer-term visa? I said, well, good idea, but how...? She suggested I marry a Chinese and smiled, we had a laugh... (note: it was all innocent).
NEVER would anything similar happen at the visa office in Hong Kong, not in a thousand years.

Update: it is no longer possible to pick up the work visa in any other place than either Hongkong or your home country, and from sometime next year you can only get it from your home country.

@veravdn: "no longer possible to pick up the work visa in any other place"

Where did you hear this from?

Did they mention, if that is the case even if Work Permit Notice says you would apply in consulate X (where X is not your home country)?

Yes, I had to change the application: I had listed Chiang Mai consulate but had to change it to either Hongkong or the Netherlands. This is coming from Wuhua HR bureau, where I applied for the permit.