Staying in makka on the third night of haj

Insha-Allah, i am going for haj this year. On the third day we will proceed to Makka for Tawaaf Ziyarah, Complete Damm-Shukar and thereafter come out of Ihraam (our base will be in makka and not azziziyyah).
Is it permissable to stay in makka on the third night and then proceed to mina on the forth morning? And which is better, i.e., to stay the third night in mina?