I am thinking specifically about the chat rooms where it would be useful/interesting to know a user's local time - perhaps alongside their name or in the user info pop up window.
If the latter then perhaps this could be a site-wide thing as it would highlight the international nature of the SO communities.
If a user did not want this info displayed for some reason there could be an opt-out/in mechanism.
For the Q&A sites, I don't really see the value – and if you must know, and the user has filled their location field, you can deduct their (at least approximate) time zone from that. If they don't share their location information, they probably don't care about sharing their time zone either.
Chat, on the other hand, already does something even better: It shows you when you can expect the user to be active.
Clearly, at this very moment (the red line), you're about to reach the peak of your average daily activity, so chances are good that I find you online in chat. Even higher chances would be Tuesday and Wednesday.
Your profile just tells me you're in England, so currently you're probably UTC+1. But that doesn't tell me when the best time to meet you online is (maybe you generally chat in the morning? During work? Late at night?). The activity histogram does give me that information.
BTW: Yes, my QR code reader works!
