There is a long tradition within monasticism and Christian asceticism of waking to pray in the middle of the night. Some argue that an interruption to our sleep in the middle of the night is natural, that eight solid hours is a modern invention after we extended our bedtimes far past the onset of darkness. Whatever the case, waking to pray in the middle of the night can be an incredibly peaceful experience of unique time with God.
If you tend to naturally wake up at some point during the night then go ahead and get up and go pray–light a candle, read through the Psalms, sit in silence. If you don’t naturally wake up at some point, then set an alarm for 2 am and pray at that time.
Pray for fifteen minutes or so and then return to bed.