Are 10,000 won dormitories in Chiang Mai better elsewhere than in Old Town?

Is somewhere else better? Maybe Nimman Haemin?
Do bedbugs appear in the Old Town, i.e., inside the city walls?
I heard the quality isn't great.
Is it better to just go to Santitham, a more modern area?
I'm going for 2 weeks.
Traveling alone as a woman.
Is the quality really that bad for places under 10,000 won?