In Massie's book "Nivholas and Alexandra" they tell that GD Olga Alexandrovna regulary took her nieces (Olga, Tatiana, Maria and Anastasia) to dinner with Maria Feodorovna (every week if I rememeber!) After that, Olga arranged little parties for OTMA, with suitable young people to play and dance with.
I have read that her oldest grandchild, Irina, was MF's favorite although.