No time of the day or night is unsuitable for reading the Qur'an, nor is there any physical posture in which you may not do so. Allah says:
‘Remember the name of your Lord at morning and in the evening and part of the night’ (al-Dahr 76:25).

‘Those who remember God when they are standing, and when they are sitting and when they are lying ‘(Al 'Imran 3:191).

Reading the Qur'an is certainly the best way to remember Him. The Companions and those who followed them, says al-Nawawi, used to read it during all hours of the day and night, whether they stayed in one place or were travelling.