Make it easier to display Dates and Times in site visitor's timezone

Currently Liquid can be used to display the UTC times from the database in a particular timezone:
{{this['Date Field'] | strftime: "%A %d %B at %I:%M %p %z", "Australia/Darwin"}}
But if you want to work out the visitor's timezone, it's necessary to implement a JS solution.
Graham Boyd has requested we build a feature which uses best practice JS but is quick to implement and re-usable.