I'm building my parents a computer and they have this fairly enclosed little nook for the computer with the opening in the front being the only way air can move. I was hoping someone knew of a good case (if there is one) for something like this. preferably <$75 mid tower.
Unless it's low end, low power or whatnot, and produces little heat, that's not usually a good idea. Almost all, if not all cases are designed to have air flow through the case, and not usually a loop around the case to exit the same side it entered.
Reverse the air flow and have the fan in the back facing in and a fan in the front facing out. An Antec 300 would manage this. The only issue would be if you plan to use an enclosed video card with an exaust in the back. There are plenty of cards that don't do this, though.