The 3rd of June 2015.
It is on the second Monday in October, which in 2015 is Monday the 12th of October.
From the day the question was asked and answered, Friday the 10th of October 2014, it is 34 weeks and 3 days until Monday the 8th of June 2015.
To determine the specific day 93 weeks ago, you would need to know the starting date.
2015 will have 52 weeks and a day, just like all the other non-leap years.
Friday.
October 21st
Well today is Sunday 23rd August 2015, so in two weeks (that is 14 days time) it will be Sunday 06th September 2015.
Adding five weeks to October 13 gives November 17.
Columbus Day
26 weeks (and one day).
Usually a Saturday afternoon in September, however for the 2015 season the Grand Final will be held in October, which has only happened once before ever.
New Year's Eve 2015 is the last day of 2015. New Year's Eve is the day before the new year. Just like Easter Sunday 2015 or Christmas Day 2015 etc. are in 2015, New Year's Eve 2015 is also in 2015. It is not the New Year's Eve that is the eve of the start of 2015, which is where a confusion might arise leading to your question.