There is a type of Christian Contemplative prayer called Centering Prayer, based on the book, "The Cloud of Unkowing," where you keep your mind open to God.
Sometimes during the day I try to get in touch with what Karl Rahner calls the Infinite Silence, which is the silent Presence of God. It is a kind of listening to the "still small voice of God."
Also, the Eastern cultures once knew more about meditation than the west. So, I don't see anything wrong with adapting certain Eastern methods like concentrating on the breath to help reach a quiet state.
There is also the Jesus Prayer, and a great book about it called "The Way of the Pilgrim," in which is repeated the following (or variations of): "Lord Jesus Christ, have mercy on me."
In this day and age of business and rushing around getting things done, there is a need to quiet the mind.
Lastly, a great way to quiet the mind is to pray the Psalms.