Praise be to Allah.
There is no saheeh hadith about the virtue of looking at the Ka‘bah, and simply looking at it is not an act of worship for which a person will be rewarded. But if looking at it is accompanied by thinking about the splendour and majesty that Allah has instilled in it, and how people long to come to it from the ends of the earth, then this is something good that is islamically prescribed, and there is nothing wrong with it, whether that is during tawaaf or otherwise.
At-Tirmidhi (2032) narrated, in a report that he classed as hasan, that Naafi‘ the freed slave of Ibn ‘Umar said: One day Ibn ‘Umar looked at the House – or at the Ka‘bah – and said: How great you are and how great your sanctity, but the sanctity of the believer is greater before Allah than you. Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
Looking at the Ka‘bah is not an act of worship. Rather if, when looking at the Ka‘bah, the individual intends to reflect upon this venerated structure to which Allah has commanded His slaves to make pilgrimage, and increases in faith as a result of this reflection, then this is what is required in this regard. As for merely looking at it, that is not an act of worship.
End quote from Majmoo‘ Fataawa wa Rasaa’il al-‘Uthaymeen (24/18)
See also the answer to question no. 96079
See also http://islamselect.net/mat/71976
And Allah knows best.