All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
We will summarize for you what the scholars said regarding the place where the person should look at while praying, while bowing and otherwise:
The Fiqh Encyclopedia reads:
“Looking at the place of prostration in prayer:
The Shaafi'i and Hanbali Schools of jurisprudence are of the view that it is a Sunnah for the praying person to look at the place of prostration during all his prayer as Abu Hurayrah narrated that the Companions of the Prophet used to raise their eyes to the sky in prayer, and when Allaah revealed the verse: {They who are during their prayer humbly submissive.} [Quran 23:2], they looked at the place of prostration because looking at one place is more submissive and humble and the place of prostration is more honorable and easier to look at. Ahmad said in the narration of Hanbal, 'Submissiveness in prayer is that one looks at the place of prostration...' The Shaafi'i scholars said, 'This is in other than the funeral prayer, but in the funeral prayer, one looks at the dead (his coffin).' The Shaafi'i School excluded from looking at the place of prostration in prayer when one is in Tashahhud, as the Sunnah when one raises his index finger is that his eyesight should not exceed looking at his index finger... Al-Baghawi and Al-Mutawalli asserted that the praying person looks at the place of prostration when standing in prayer, at his feet when bowing, at his nose in prostration, and at his lap when sitting because looking around distracts the praying person [from concentrating in the prayer], so it is more appropriate to look at one place... The Hanafi School considered looking at the place of prostration and other places [as described] as part of the etiquette of prayer... The Maaliki School, as cited in Minah Al-Jaleel and Sharh al-Kharashi, says, 'It is disliked to look at the place of prostration as this leads him to bow down his head; rather, he looks in front of him ... but some scholars of the Maaliki School consider that looking at the place of prostration is recommended.” [Abridged]
For more benefit, please refer to fataawa 187811 and 106203.
Allaah knows best.