He is asking what he should do after performing ‘umrah because he will be staying in Makkah for a few days

Firstly:

We ask Allah to make it easy for you to do ‘umrah, and to help you to perform it and accept it from you.

Secondly:

Ifafter doing ‘umrah you are going to stay for a few days in Makkah, our advice to you is to do a lot of righteous deeds, as much as you can, so that you can benefit more from this virtuous place, because the reward for good deeds is multiplied in places and times of special virtue, as was confirmed by the scholars (may Allah have mercy on them):

ar-Ruhaybaani (may Allah have mercy on him) said:

Good and bad deeds are multiplied in places of special virtue such as Makkah, Madinah, Bayt al-Maqdis (Jerusalem), and in the mosques; and at time of special virtue, such as Friday, the sacred months, and Ramadan.

End quote from Mataalib Ooli an-Nuha (2/385)

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:

Prayer in Makkah is undoubtedly better than prayer anywhere else, hence it was narrated that when the Prophet (blessings and peace of Allah be upon him) was staying in al-Hudaybiyah during the campaign of al-Hudaybiyah, he was in the area outside the boundary of the Haram (sanctuary) zone, but he used to pray within the boundary of the Haram. This indicates that praying in the Haram – i.e., within the boundary of the Haram zone – is better than praying outside the boundary of the Haram zone, and that is due to the special virtue of that place. On the basis of that, the scholars adopted a principle in which they said: Good deeds are multiplied in every place or time of special virtue.

End quote from Majmoo‘ Fataawa Ibn ‘Uthaymeen (20/168).

There are acts of worship that are of special virtue in al-Masjid al-Haraam, including prayer. One prayer in this place is better than a hundred thousand prayers offered in any other mosque. So you should be keen to offer the five daily prayers in congregation in al-Masjid al-Haraam.

Another of these acts of worship is tawaaf. Many of the scholars are of the view that doing a great deal of tawaaf, for a stranger in Makkah, is better for him than offering a lot of voluntary prayers, because prayer is something that the Muslim can do in any place, but in the case of tawaaf, the only place it can be done is around the Ka‘bah.

Al-Bahooti (may Allah have mercy on him) said:

It is Sunnah to do a great deal of tawaaf all the time. We have quoted above the statement of Imam Ahmad that tawaaf, for a stranger, is better than prayer in al-Masjid al-Haraam.

End quote from Kashshaaf al-Qinaa‘ (2/485)

He (may Allah have mercy on him) also said:

Imam Ahmad stated that tawaaf, for a stranger, is better than praying in al-Masjid al-Haraam, because it is unique (to that place) and he will not be able to do it after he leaves, unlike prayer.

End quote from Sharh Muntaha al-Iraadaat (1/237)

It says in Fataawa al-Lajnah ad-Daa’imah (vol 2, 10/355):

What is prescribed for the one who comes to Makkah and has completed his rituals is to do a great deal of tawaaf in particular, and to read Qur’an, pray, give charity and do other acts of worship. End quote.

Shaykh Ibn Baaz (may Allah have mercy on him) was asked:

Is it better to do tawaaf repeatedly or to offer voluntary prayers?

Answer: there is a difference of opinion as to which is better, but what is best is to combine both matters, so he should offer a lot of prayers andd a great deal of tawaaf, so as to combine two good things. Some of the scholars give precedence to tawaaf in the case of strangers, because they do not find the Ka‘bah in their homelands, so it is mustahabb to do a great deal of tawaaf so long as they are in Makkah. Other scholars give precedence to prayer, because it is better than tawaaf. What is better in my view is to do a great deal of both, if one is a stranger, so as not to miss out on the virtue of either of them, and attain the reward of both.

End quote from Majmoo‘ Fataawa Ibn Baaz (17/225)

Similarly, there are study circles in al-Masjid al-Haraam where one can learn about fiqh, ‘aqeedah and hadith, and other shar‘i sciences, according to the way of Ahl as-Sunnah wa’l-Jamaa‘ah. So you should be keen to attend these study circles and ask about whatever you need to know of religious matters, for these study circles are not available in every country.

To sum up the above, the Muslim should strive to make the most of his visit to those holy places, so he should do a lot of righteous deeds, such as prayer, tawaaf, seeking knowledge, reading Qur’an, dhikr, and du‘aa’, for the time is short but the rewards for one who is sincere in his intention and who does good deeds are great, in sha Allah.

And Allah knows best.