Does Hex Crawling Entirely Within A City Work?
That depends on where you live...I've been without a vehicle at a few points in my life, I live in a suburban area...the nearest store WAS a little over half a mile away (it's since closed and is now a Vasa Fitness Center, the nearest store is now about 3/4 of a mile away).
But given that humans walk at between 2 and 4 mph (on average), going anywhere that's a mile or more away requires some kind of incentive, just because of the time commitment involved (like getting my car back from the shop, which is another mile past the grocery store mentioned above...when I have to get work done on it, if it isn't something they can get to immediately, I walk home and then walk back when they call to tell me the car is done...it's a hike, and it's not something I would do on a regular basis without some pressing reasons to do so.)
But back to the question at hand...I don't see why you couldn't treat a cityscape as another type of terrain to explore (which is what I take the term 'hex crawl' to imply). The trick is coming up with a motivation for it, which can be dictated, so some extent, by the setting.
--Post-apocalyptic survival setting? You bet, no problem, especially if your PCs don't have any sort of established base that they're operating out of and therefore need to daily scavenge for necessities.
--Fantasy setting? Could be...are they trying to locate a specific type of shop? Looking for some kind of den that a creature has set up? Just moved into the city and are trying to get a handle on the neighborhood and who's in it?
--Horror? Certainly...which house is the nearest witch/mage/vampire inhabiting? Is there a sewer access that giant snakes or Pennyworth can creep out of and snatch victims? Does someone's house have just a few too many exotic plants growing around it that could be housing some kind of creature? Is the cornerstone of some building in town actually an ancient altar to the Elder Gods that some cult uses for sacrifices on special occasions?
You can do just about ANYTHING, in any game or setting, provided you can come up with a logical motivating factor for doing it (as opposed to basically saying, "Here's a sheet of paper...this is town. It's blank because you don't know anything about it. Go explore.")