Time is limited during Hajj. The perfection of the Hajj includes not wasting any time. One of the most important and fruitful uses of time during Hajj is the remembrance of Allah. This is hinted at in the verses of Hajj revealed in Surah Baqarah (196-203), where the remembrance of Allah is mentioned 4 times to emphasize the importance remembering Allah. Allah says, “So when you have emerged from Arafat then remember Allah at the Sacred Spot (Muzdalifah); and remember Him as He has guided you for surely you had been misguided before” (2:198). Here, the remembrance of Allah is encouraged post-Arafat at Muzdalifah. Also mentioned in the verse is a key element of remembrance of Allah: remembering Him as He instructed through the actions of the Prophet.
Some ways to remember Allah are: reading the Quran, reciting the talbiyah excessively, repenting from sins, repeating the Prophetic invocations and making lots of dua. Some times where Allah specifically encouraged His remembrance is at Arafat, after Arafat at Muzdalifah (2:198), asking for forgiveness after emerging from Muzdalifah (2:199), after completing the rituals of Hajj (2:200) and during the stay at Mina (2:203).
To put this to practice, set some goals for Hajj. For example, aim to read a juz a day during Hajj. Carry a pocket-size mushaf throughout the Hajj and read it during the times when waiting to proceed from one step of the Hajj to the next. Another goal could be to make a specific dhikr a specific number of times as instructed by the Prophet. (e.g. subhan Allahi wa bihamdihi 100 times in the morning and evening).