I went to OfficeMax and Staples and sat in every chair they had. The fifth-to-last chair I tried at Staples ended up fitting me perfectly. I think it was $100. I ended up turning the arms upside-down because I don't use them but they're still required to keep the back from breaking off.
Before going, I had researched the proper ergonomic position for a computer user. The important parts were legs at ninety degrees, chair can't put pressure on underside of your hamstring muscle (otherwise blood pools in your leg), lumbar support, and (for me, at least) vertical neck support allowing me to read the monitor while my neck muscles are completely relaxed. To complement this, I built a two-tier desk where my elbows are at 90 degrees while using the keyboard. I also have a wireless mouse[1] to use when sitting in a different position (because different positions are the key to being comfortable).
EDIT: Guess I should have read the $200 limit. I know of no chairs in that range which are any good. If you're going for $200, you might as well shoot for $50-75 and get something cheap from Office Max; I don't think the extra $100 or so would buy you anything much better. You could probably get an improved surface type (leather instead of pleather, etc.) but that's probably it.
==== HERE BE EXPENSIVE CHAIR ====
I love my Humanscale Freedom (get the headrest, too). It has gotten to the point now where I can't really sit in anything else without my back killing me because I've become so used to the perfect support it provides.
Definitely pricey (mine was $1,200 I believe, after a $200 rebate), but wow has it been worth it. The only complaint I have is that the quality of the arm rest connectors are pretty poor; I had to have a replacement shipped after I leaned on one while getting up and snapped the thing off. My ~160 lbs frame shouldn't do that.
When I was chair shopping I found that good chairs started at around $300. Assuming your definition of good includes "adjustable". As far as I know under $200 means either non-adjustable or craptastic.
Next time I have a chance to buy a chair I'm going to consider the Aeron. Having to fidget every 5 minutes because the chair's not comfortable has an annoying habit of making me forget exactly what I was just doing, and the Staples/Office Depot chair du jour always seems lacking.
Mine were on sale - I got two for like $120 each. It was good because they were exceptionally comfortable, durable, and they looked quite good with the rest of my kit. I'm normally Captain Frugal, but I spent a bit to my home office together since I had a lot of people coming through there and making a good impression was a definite plus.
If you have a Crate and Barrel near you, might want to poke around there and ask when their next sale is happening. Durable, comfortable, and clean modern aesthetics is my kind of thing.
Before going, I had researched the proper ergonomic position for a computer user. The important parts were legs at ninety degrees, chair can't put pressure on underside of your hamstring muscle (otherwise blood pools in your leg), lumbar support, and (for me, at least) vertical neck support allowing me to read the monitor while my neck muscles are completely relaxed. To complement this, I built a two-tier desk where my elbows are at 90 degrees while using the keyboard. I also have a wireless mouse[1] to use when sitting in a different position (because different positions are the key to being comfortable).
[1] The Perific wireless mouse http://www.thehumansolution.com/perificmouse.html which I just discovered is discontinued. sorry, and I really hope mine doesn't break.