This title has been published on and off since 1996. The original mini series (6 issues) was very good, although quite serious. The later series have varied in tone, so some issues have gone for a lighter touch, but there have also been several which are very moving, bordering on heartbreaking. It's been on hiatus for a while, but it's now back with a new ongoing series. Issue #1 was ok; it certainly wasn't a bad comic, but it didn't really stand out either. The main thing that struck me was the passage of time: unlike most comics (e.g. Marvel/DC), Astro City basically runs in real time. So, characters who last appeared as young children are now adults with jobs, which is a bit scary!
Issues #2 and #3 are a 2-part story. I was initially surprised that #2 didn't really follow on from #1, but I think that's for the best. This is a story which really shows what Astro City is all about. Basically, it's about the superhero equivalent of 999 despatchers. Using familiar characters as an analogy, if there's a cat stuck up a tree in Metropolis and Lex Luthor is planning to set off a nuclear bomb in California, which call is more important for Superman to deal with? You don't need to have read any previous issues to understand what's going on. If you watched Avengers Assemble then you'll understand the concept of a superhero team, and that's all you need to know.
Meanwhile, a couple of people have posted links to a New Statesman article: I hate Strong Female Characters. In brief, the author is saying that female characters in fiction should be nuanced, rather than being the stereotypical "Strong Independent Woman".
Reading the Astro City story, I really liked it on its own merits. It then occurred to me afterwards that this story avoids all the issues that the New Statesman article complained about. The protagonist is female, and so are several of the other characters. Although this story is set in a world with superheroes, the lead character doesn't have any superpowers, or wear a costume, or punch anyone. Basically, it's a compelling story about a character with human hopes and failings, who just happens to be a woman.
Anyway, I highly recommend the latest 2 issues. If you're new to the series, my advice is to skip issue #1 and go straight to #2. Digital comics make this whole thing much easier than it used to be: you don't need to walk around comic shops trying to find somewhere that still has last month's issue, or wait for the collected edition, you can get them both right now. If you're reading this then you obviously have internet access, so just hop over to Comixology: here's #2 and #3. (It's also worth noting that they have issue #1 of the original mini-series there as a freebie.) The main downside of digital comics is that you can't lend them out in the same way as paper copies, but I'm sure that I'll repurchase these issues when they get reprinted as a collection, and then I'll gladly lend that out.