Very early in the morning, while it was still dark, Jesus got up, left the house and went off to a solitary place, where he prayed. Mark 1:35 (NIV)
"In the Bible many godly men and women rose early to meet with God, including Abraham (Genesis 19:27), Moses (Exodus 34:4), Job (Job 1:5), Hannah and Elkanah (1 Samuel 1:19), Jacob (Genesis 28:18), David (Psalms 5:3; 57:7,8)."
(This devotional is adapted from Rick Warren's Bible Study Methods.)
Give God the best part of your day, when you are the freshest and most alert. Don't try to serve God with your leftover time. Remember, too, that your best time may be different from someone else's.
For most of us, however, early in the morning seems to be the best time. It was Jesus' own practice to rise early to pray and meet with the Father: "Very early in the morning, while it was still dark, Jesus got up, left the house and went off to a solitary place, where he prayed" (Mark 1:35).
You might even consider having two quiet times (morning and night). Dawson Trotman, founder of the Navigators, used to have code letters for his night quiet time: HWLW. Whenever he was with a group of people at night or home with his wife and the conversation seemed to be ending, he would say, "All right, HWLW." HWLW stood for "His Word the Last Word"; and he practiced that through the years as a way of ending a day with one's thoughts fixed on the Lord (from Daws: A Man Who Trusted God by Betty Lee Skinner).
Whatever time you set, be consistent. Schedule it on your calendar; make an appointment with God as you would with anyone else. Make a date with Jesus!