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

Praise
be to Allah

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.