What Antigua, Guatemala is to Spanish, Sana'a, Yemen is to Arabic - a mountainous enclave where cultural and linguistic immersion can be had on the cheap. Not only is the Arabic instruction the least expensive in the Middle east, it's highly intensive as well - most male instructors actually wear traditional jambias (curved daggers at the waist) to class. This, my friends, is old time Arabia. No 'Arabia Lite' like you find in Dubai, Sana'a is the real deal, uncut and nearly always adulterated by 'qat' (a low grade narcotic chewed every afternoon by just about everyone).
You're stepping into an ancient land and culture unlike any other on this planet. I am hesitant even recommending this place because selfishly I want it to stay just the way it is, untouched by modern influences. Forget the warnings.. mix with the locals, dress in the local garb, buy yourself a Jambia (dagger), fill your cheek with Qat, and you'll have no problem!