Is it permissible to spend the night in Makkah and then perform Umrah on the day following arrival, or must it be on the same day as entering into Ihram?

If a pilgrim performing Umrah assumes ihram from the miqat, he may delay the Umrah as long as he wishes, provided he remains in his ihram garments and abstains from what a pilgrim in ihram must abstain from. It is not a condition to perform Umrah on the same day of arrival in Makkah. There is no difference in this regard between men and women.