Yeah it's not that surprising that Brooks Bros would charge more than average for alterations. It's like getting your car serviced at the dealership - but you wouldn't bring your Honda to the BMW dealer.
Being in/near LA, I'd imagine you're in a good place for finding a good price to service ratio, what with the garment district and all that. But spending $200 to take a suit from "doesn't fit" to "fits" is not really that much overall.
One word of caution, however: there are golden proportional rules to garments that you don't want to break because you'll throw the balance of the entire piece out of whack. An easy one to highlight is jacket length. If you shorten a jacket to the point that the pockets are too close to the bottom of the jacket, it won't look right, even if it's now the right length for you. Let's call that distance 9" from the top of the pocket to the bottom of the coat, to be safe, but one of the tailors on here can tell you their magic number.
I'm actually in orange county which is about 2 hours from central LA depending on traffic. I did find a local tailor that seemed to get good ratings on yelp and his prices fell in line with the previous posted link. He is a small shop and spent about 30 min getting me sized and told me if the suit is 2 long or too wide in the shoulders he wouldn't bother taking my money, because it would be 1. Too costly to make the alterations and 2. The finished result wouldn’t look right. Here is what I have being done. take in the sides a couple inches, shorten the sleeves an inch or so take 1” off from the bottom, 1” in on the pants and put a him on the pants. Total out the door was $125. I pick it up Wed so hopefully it will fit nice.