I have written this script: [StackExchange sites - convert dates to local timezone ][1].  
It applies to Stack Exchange sites, e.g. : stackoverflow.com, stackexchange.com, superuser.com, etc.

The timezone that [the Stack Exchange sites use is UTC][2] i.e. +0000.  
So, this script converts the dates to your local timezone, in both:  

- tooltips `2015-12-14 14:11:13Z`, and in  
- date text like `Dec 14 '15 at 14:11` or `Dec 14 '15 at 14:11`.  [superuser.com][3]

It also recalculates them whenever the page changes via `MutationObserver`.

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Known issue:

 1. While you are on the superuser.com homepage, every 1 minute the activity indicator which will show when new posts are asked or answered.  
  Also, every relative timestamp, e.g. `answered 1 min ago` will become `answered 2 min ago`, and so on.

  Well, while using the script, the latter feature, i.e. "*the relative timestamps being increased every 1 min*" becomes broken, and they don't get updated anymore.


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The script modifies the values as follows (in my case, for timezone EEST, +0200):  

- tooltip: `2015-12-14 14:11:13Z` --> `2015-12-14 16:11:13`  
- date text `Dec 14 '15 at 14:11` --> `Dec 14 '15 at 16:11`

If I try to add a `Z` to the modified tooltips, i.e. modify the line 65 to:

    dates[i].title = toTimeZone(temp, localTimezone) + 'Z';

therefore the text in the above case to become `2015-12-14 16:11:13Z`  
then the page hangs (the `MutationObserver` constantly sees mutations ).

The other approach I tried, was *(instead of modifying all tooltips+texts on page)*,  
to attach an event listener on each, 
to be activated on `onmouseover` and be restored on `onmouseaway`, but I found it very difficult to implement.


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<br>
*It uses the `jsTimezoneDetect` script (for getting the local timezone),  
and `Moment.js` and `Moment-Timezone` JavaScript libraries (for converting the dates).  
Also note: `jsTimezoneDetect` does not do geo-location, nor does it care very much about historical time zones, e.g. it may get "Europe/Berlin" when the user is in fact in "Europe/Stockholm" (they are both identical in modern time).*  


  [1]: https://greasyfork.org/en/scripts/14918-stackexchange-sites-convert-dates-to-local-timezone
  [2]: https://meta.stackexchange.com/questions/2941/why-are-the-time-stamps-in-utc-instead-of-localized-for-the-client
  [3]: https://superuser.com/