* Multiple equivalent GMTs (GMT, GMT (Greenwich Mean Time), GMT + 0)...
* GMT+n would ideally be in numeric order [but alpha sort doesn't make this easy, just something to think about]
* Include country name for cities: "Seattle (USA)" ... just gives you that warm fuzzy that you're in the right country.
* Instead of "next day" it might be nice to say "next morning/afternoon/evening/night" or whatever it happens to be. Less mental parsing ("12:30am next day... means really early in the morning right?")
Anyway, great job!