An 80 year tradition has the Holy Father taking a Lenten retreat usually within the first week of Lent.
Here is last year's notice:
"Continuing an 80-year-old papal tradition, Pope Benedict XVI is canceling regular audiences and clearing his calendar to make a weeklong Lenten retreat. The spiritual exercises not only shut down the normal business of his pontificate, but also place the pope in the unusual position of doing all the listening and none of the talking."
This year's retreat is scheduled from March 1st through the 7th.
I do not believe the Holy Father will be making any announcement on the Archbishop of New York appointment during this time. It is not business as usual, the normal business is "shut down." In addition, I do not believe he will make the announcement from Ash Wednesday, February 25th, to March 1st, as it is might prove too distracting for beginning of the Lenten season. This would also be considered a celebratory announcement, which would be in conflict with the traditional Lenten theme.
So we are left with early next week, or after March 8th. Early next week would make sense as the Catholic Church in America would have heighten exposure going into Ash Wednesday, and the Vatican probably wants to clear it work load before shutting down for a week.