While Jesus did spent a lot of time with his disciples and in teaching. He also had time everyday alone where he spend in prayer (Mk 1:35, 14:23, Lk 5:16, 6:12,13, 9:28, Mt 14:32, etc). He modeled what it means to have an intimate relationship with Jesus and he modeled the principle in Psalm 46:10 (NIV) which says, “Be still, and know that I am God."
Another concept to realize is that our bodies are important:
1 Corinthians 6:19, 20 (ESV) asks "do you not know that your body is a temple of the Holy Spirit within you, whom you have from God? You are not your own, for you were bought with a price. So glorify God in your body. " We need to take care of our bodies.
Finally, a key principle from a Biblical perspective is in regards to the Sabbath, a day of rest for the Christian. The Christian is called to keep this day of rest, holy (Ex. 16:23, Is. 58:13, etc).
Is this still true for in the New Testament?
There remains, then, a Sabbath-rest for the people of God; for anyone who enters God’s rest also rests from his own work, just as God did from his. Let us, therefore, make every effort to enter that rest, so that no one will fall by following their example of disobedience. (Hebrews 4:9-11)
Does it have to be Sunday? Not necessarily. John Piper puts it this way (2013):
"Now I think that the principle in the New Testament (Rom. 14 particularly) is that God ordains that one day in seven be restful. I think that's a creation ordinance for our good, for our health."
The key is on the importance of rest, God even had a day of rest after Creation, we too need to rest in order to be our best the rest of the week!
References:
Piper, J. (2013). What does it mean practically to keep the Sabbath Holy?Retrieved from http://www.desiringgod.org/resource-library/ask-pastor-john/what-does-it-mean-practically-to-keep-the-sabbath-holy