I recently had to extend my 30 day visa exemption by another 30 days. Last time I was here, I went to Promenada mall on the south east side of Chiang Mai. As of September 2018, Promenada mall immigration office closed down and replaced with one by the airport.
It's relatively easy to get to. I cycled there in 15 minutes using a Mobike -- although you do have to cycle down a dual carriageway. Of course, you can always get a songthaew or Grab. But at least the options are better than for going to Promenada.
This place was busy. I arrived when it opened at 08:30, and the place was already jam packed. When I went to Promenada, I was in and out in 20 minutes. I ended up spending 1.5 hours at this place, and some of my friends spent much longer.
I needed to get some photocopies of my passport and visa and found out the building on the other side of the main road -- the white one that looks like a spa -- can do them for you. But they are incredibly slow. Maybe like 1 person every 5 minutes. I'd recommend getting photocopies somewhere else. There are a ton of places in south Nimman, on the way to the university.
The procedure was pretty much the same as before; hand in all the documents, receive a ticket, wait until you're called and then go up for a photo, sit down back and then finally go up to get your extension.
I'd also be sure to check out the calendar of public holidays and not just blindly assume the chances of going on a holiday are slim... I made that mistake.