I'd be shocked if you can't find qat at these places. It's worth a try; I'd describe it as amphetamine salad. It's at about the midpoint between a strong cup of coffee and adderall.
An odd thing about qat is that despite being a stimulant it fills the role of alcohol in Yemeni culture—it's what men blow their salaries on, go on benders with, sometimes even destroy their families over. It's fascinating to see a drug with completely different physical effects exhibit so many of the same social pathologies as alcohol.
Don't chew it too often or it will stain your teeth.