/C Broken - $690 to repair reasonable
That does sound reasonable. My mom got her AC worked on by a dealer in 00' when she was going through a divorce. Anyway, she paid $1500 + for them to do a simple recharge and fill.
The rate for labor is $75 - $100 AN HOUR. Check online for prices on the parts and then add labor. I don't think $690 sounds unreasonable at all. I know from experience I would pay a little more for quality work. I would be more concerned about the reputation of the shop than to save $50 bucks.