As almost everyone knows, Adam's Apple has been closed for years. There are persistent rumors that it will be re-opened, but those have been going on for years as well.

Other places:
Doi Boy -- a nice name, but I never go there and I don't know anyone who does.
Circle Pub -- this is the "upscale" gay bar in Chiang Mai, but the guys working there are a mix, just like other places. I don't care for the show, and never have.
Free Guy -- aside from Circle, this is the most popular bar in Chiang Mai. The show features extensive nudity but no sex.
My Way -- this bar went seriously downhill after the star left and opened his own restaurant. He was not only the star, he was the one who thought up all the shows, rehearsed them, and then monitored them every night. His restaurant is doing very well (serving Shan food a few steps away from My Way, but a gay karaoke place at night). He heard of the troubles of the old place, and has returned on a part-time basis -- so I need to take another look, soon.
The Garden Bar -- outside the closed Adam's Apple. It's a place for farang to meet other farang, like Soho (is that still open?)
The Night Bazaar bars -- I guess Cream Bar is the most popular. These bars are less costly than the other places in Chiang Mai.
Coffee Boy -- I hear it's closed, but I really don't care! :-0

To make this even shorter, I'd recommend "My Way" and "Free Guy," period.