Taken during the IF's visit to Romania, 1913 or '14.
Right, I'm guessing the latter half of 1913 or very early 1914, at the latest, for a few reasons...
1) The baby, Prince Mircea, was born in January of '13 and looks to be under a year.
2) King Carol I died in October of 1914 so it obviously couldn't be after then.
3) Princess Ileana was born in January of 1909 and could probably been around 4 1/2 in this photo (although she looks a little older than that to me)
4) Maria Nikolaevna still has her down. I think the family started allowing her to wear it up not long after her 15th birthday even though 16 was the traditional age. If this photo were taken in the autumn of 1913 Tatiana would have been sixteen but Marie around 14 1/2.