Praise be to Allah.
The Sunnah for the one who goes to Makkah for Hajj or ‘Umrah is to start first of all with al-Masjid al-Haraam and do tawaaf (circumambulate the Ka‘bah) before he goes to any other place. That is because of the report narrated by al-Bukhaari (1642) and Muslim (1235) from ‘Aa’ishah (may Allah be pleased with her) who said: “The first thing he (blessings and peace of Allah be upon him) did when he came to Makkah was to do wudoo’ then circumambulate the House.”
Al-Nawawi (may Allah have mercy on him) said: The hadeeth of ‘Aa’ishah was narrated by al-Bukhaari and Muslim. Our companions said: As soon as he enters Makkah, he should not try to find a place to stay or change his garments or do anything else except tawaaf. Rather some of the group should stay with their luggage and mounts so that the others can perform tawaaf, then they should come back to their mounts and luggage and find accommodation. End quote from al-Majmoo‘, 8/15.
Imam al-Shaafa ‘i (may Allah have mercy on him) said: We have not heard that when he entered Makkah he stopped at any place, either in his Hajj or his ‘Umrah, until he entered the mosque, and he did not do anything when he entered the mosque, either bowing or anything else, until he started with the House and performed tawaaf. He did this in both his Hajj and his ‘Umrah.
End quote from al-Umm, 2/185
From the above it is clear that the Sunnah is for the muhrim (pilgrim in ihram) to start the rituals from when he reaches the Haram, following the example of the Prophet (blessings and peace of Allah be upon him) – as stated above – and because leaving a long interval may be a cause of committing some of the actions that are forbidden whilst in ihram.
But if a person is very tired because of having travelled a long way, and he delays ‘Umrah so that he can rest, there is nothing wrong with that. Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: If a person comes to Makkah and is tired, and he is not able to perform ‘Umrah until the following day, what is the ruling on that? Is it essential to perform ‘Umrah as soon as one reaches al-Masjid al-Haraam?
It is best for the person who has come to do ‘Umrah to start, before anything else, by doing ‘Umrah, even before he goes to his accommodation. So he should perform ‘Umrah because that is the purpose (for which he came). But if he delays it, especially if he is tired, so that he can rest, there is nothing wrong with him doing that and his ‘Umrah is still valid.
End quote from Majmoo‘ Fataawa al-Shaykh, 22/285
And Allah knows best.