For $100, go to used furniture places, garage sales, thrift stores, office surplus places, and anywhere you can find older chairs.
The older ones are often built substantially better than the new ones. Most of them have been snapped up by now, but you used to be able to find solid oak office chairs well under $100. Most need to be refinished (easy, but takes a few hours) but make comfortable and incredibly durable office chairs. The steam-bent oak ones are surprisingly comfortable, as well, if you can find them.
The other alternative is to look for the steel ones from the 1950s-1970s or so. Steelcase and others made massively overbuilt chairs that can survive being thrown off the roof.
Most of those will have hideous and/or damaged upholstery. The good news is, again, that upholstery is simple. You can find any number of guides online or books at the library. It doesn't require skill or expensive tools, you just have to be willing to sit down for a few hours and work carefully. You can find fabric, foam and other supplies cheaply at local fabric/upholstery shops.
Even though a chair might have horrible, dirty and slightly torn houndstooth naugahyde upholstery from the Seventies, think about how it would look replaced with new black leather. Don't be intimidated - you can put the leather on yourself and end up with a chair worth considerably more than $100.
Edit: You want to look for something like this:
Imagine that recovered with the leather of your choice. You can also find good deals on upholstery at eBay
. Again, it'd be a simple matter to put black leather on this chair. It would last for years, and then you could reupholster again when it needed it.