Judging by the lack of response to this thread I'm guessing there aren't many Hyde Parkers on LTH, but in general I think Z&H deserves more hype than it gets. As others have said, the sandwiches are creative and always tasty -- my personal favorites are the Jamon, Jamon (mentioned above), the Bernita panini (Manny's corned beef, swiss, dijon, and house-made chutney on rye), and the Lil Smoky panini (turkey, brie, chutney, and curry mayo on wheat). They also use Metropolis coffee and make great lattes, cappuccinos, and chai.
I think very few people have realized how good the bagels are, though. All the discussion on LTH is about New York Bagel & Bialy, which is of course good and really authentic, but Z&H makes their own bagels in-house every morning and they're great (...and WAY closer, at least for those of us on the south side!). I'm no New Yorker, but I think they have great texture (soft but chewy), and you can get them with nova lox. My personal favorites are the salt, onion, and everything, but they also have the standard plain, poppy, sesame.
Another overlooked but great part of Z&H is BEIGNETS! Yes, beignets. In Chicago. In Hyde Park. They only make them on weekends, but they're delicious, made to order, and usually gone by lunchtime (I've been disappointed several times, but it's a good reason to get out of bed early on a Saturday!). I think they're also only served at the 57th street location, which is also the busier of the two.
Hyde Park doesn't have the biggest foodie-draw, but I hope bagels, beignets, and a good cup of coffee could lure at least a few people down here.