Converting timestamps to local time with date_l18n()

I know I’m three months late, but the function you want here is WordPress’ get_date_from_gmt().

The function accepts a GMT/UTC date in Y-m-d H:i:s format as the first parameter, and your desired date format as the second parameter. It’ll convert your date to the local timezone as set on the Settings screen.

Example usage:

echo get_date_from_gmt( date( 'Y-m-d H:i:s', $my_unix_timestamp ), 'F j, Y H:i:s' );