If you don't mind, I'd like to take a step back for a moment. Because it seems like you're not really looking for the most (or least) hyped restaurants, but instead, you're asking a different question:
How can I discover really good restaurants, without relying on "media buzz" which may rely more on hype (or overhype) than on actual good food?
Here are ways to discover restaurants to try.
One is to review the "GNR" list and recommendations on LTH. Another is just to read evaluations posted here in the "Eating Out in Chicagoland" forum on LTH. Consider those recommendations and whichever ones sound to you like you would enjoy them, go there and try them.
Consider what kind(s) of restaurants you enjoy, and try more of them. You've mentioned Chilam Balam; this is one of 10-15 restaurants in Chicagoland specializing in creative/provincial Mexican cuisine. If you like, you can try more of those 10-15 restaurants. Same thing with French bistros like Chez Joel. (You can even find a list of most of the French bistros
here on LTH.)
Try other kinds of food. The
listings on Metromix identify almost a hundred different kinds of cuisine for their restaurants, and even those have variations (for example, their "Central American" category includes restaurants specializing in Costa Rican, Guatemalan, Belizean, etc cuisine). If you've never tried an Ethiopian restaurant, then go try one and see how you like it.
Try places close to home. Just about every neighborhood in the city and suburbs has a variety of places to choose from. Even if they're not great, the convenience factor is there - and if they do turn out to be great, then you've discovered "hidden gems" yourself.
And I wouldn't discount the media entirely, either. Sometimes when a place gets a lot of hype, it's because it's actually good (which appears to be the case with the Girl and the Goat). Who cares whether or not it's hyped, as long as it's good? Just make a reservation and see for yourself.