According to
At Home with the Last Tsar and His Family, Nicholas and Alexandra moved into the newly redecorated west wing of the Alexander Palace in September of 1895. In August of 1895 Nicholas noted in his diary, "Our new rooms are still being decorated, so we are living in the old quarters."
Nicholas's diary entries throughout 1895 are labeled with Tsarskoye Selo. For example:
19 December - Tsarskoye Selo
Today our daughter was moved upstairs to the nursery - May God bless her!After the revolutionary events of 1905, the imperial family moved permanently to the Alexander Palace.
It appears that the Concert Hall may have existed until 1902 or 1903, when the Meltzer brothers created the Maple Room and the tsar's New Study. Unfortunately my sources don't discuss the arrangement of the children's rooms prior to the remodeling in the 1900's.
This architectural drawing of Aleksei's remodeled rooms is dated 1913: