Best Mathematical Date?

Guy A is planning to propose to Girl B this year. As a matter of principle, Guy A has chosen mathematically significant dates to plan momentous events. Based on years of interaction with Girl B, Guy A has ascertained that Girl B would wish to celebrate with family and friends once she (hopefully) says ‘yes’ to the proposal. Unfortunately, an important family member will be out of town until end of October and Guy A and Girl B will be traveling starting on 11/10/12. After Guy A and Girl B return from their trip, it may be too close to holiday season to uniquely celebrate an engagement. Trying to balance mathematical elegance with catering to the desires of Girl B, please recommend the best date, in the range 11/1/12–11/10/12, for the proposal to take place.

(This is for a friend… Looking for something along the lines of 11/11/11 is the last binary date but needs to be within provided date range.)