According to this article, Bhrigu Rishi tested the Trimurti of Brahma, Vishnu and Mahesh(Shiva) for who is the best God and should be worshipped. It is also mentioned in this question about him testing the Trimurti. I know from legends that he then committed penance in the guilt of kicking Lord Vishnu in the chest. What is the place where he chose to do penance? There is a Bhrigu temple in Ballia district of Uttar Pradesh, India where the locals believe that it is the shrine of Bhrigu and he performed penance there. Are the locals correct as Ballia is also known as Bhrigu Nagri or The land of Bhrigu? What is the place according to scriptures?
According to this the importance of Bhrigu Temple and Sage Bhrigu doing penance in the city of Ballia is mentioned.
This town is undoubtedly of great antiquity; many legends bear witness to its historical importance. It is a common belief that Ballia was founded after the name of Rishi Balmiki, the first Sanskrit Poet of India.
The Confluence of the holy river Ganges and Sarju at Ballia has given a peculiar Sanctity to the town for the Hindus. It is the Site of a great assemblage which continues to be held even today in the form of Dadari Fair. Another significant legend connects this town with Rishi Bhrigu. There is a fine temple in the memory ofthe Rishi in the South Eastern ofthe town. It contains the idol of Bhrigu and Dardar Muni.
The puranic legend connected with Bhrigu, has a direct bearing on the Social attitude of this area. It is said that in a conference of Gods, Bhrigu was deputed to find out, who out of the three Gods of the Hindus Trinity — Brahma, Vishnu and Mahesh was the greatest. Bhrigu first went to his father Brahma who behaved rudely with him and was chided by him; He repeated the same behaviour before lord Shiva and had been chided there too. Lastly, he went to the lord Vishnu who was then having his afternoon nap. Brig felt angry and kicked lord Vishnu on his chest saying ‘You are omniscient and know everything but you are not rising to welcome me. Lord Vishnu instead of feeling enraged, gently pressed the foot of Bhrigu and Said, ‘I hope the tender Lotus- like foot of the Rishi is not hurt while striking the stone like hard chest of mine’. And thus apologizing, he welcomed the Rishi and showed due honour to him. Bhrigu then returned to the conference of the gods and declared Lord Vishnu to be the greatest of the Hindu gods. The legend further goes that Bhrigu being struck with remorse for striking such a noble god himself, went to him and asked his forgiveness. Lord Vishnu gave him a deer skin and asked him to move around with it and settle down for penance at the place where the same would incidentally fall. The deer skin fell at the confluence of the rivers of Ganga and Sarju. This place then became the ‘Tapoban’ (place for penance) for Bhrigu who is said to have done penance for one thousand years there. It is this place which is myth logically known as Ballia.