God is our refuge and strength, a very present help in trouble (Ps 46:1).
In the Old Testament, a place of refuge was a designated place where a person that accidentally killed someone could go to escape the possible revenge of the family of the one he killed (Num. 35:6, 10-27). Once in this place, an avenger could not touch the manslayer until a trial was set and the evidence weighed. Once the facts were viewed a decision is made. If the person was killed by accident, then the slayer would be found innocent. However if this is not the case, the murderer would be release to the avenger(s) for street justice. These cities of refuge were spread out around Israel.
David was accustomed to running for his life from his enemies. Because he did not kill anyone the times he fled, he could not seek to find peace in a city of refuge. David was being pursued without justifiable cause. He did manage to find refuge, but not in a conventional place. Rather, David found a place of refuge in the loving arms of God. In the Lord David found the peace he needed.
He that dwelleth in the secret place of the most High shall abide under the shadow of the Almighty. I will say of the LORD, He is my refuge and my fortress: my God; in him will I trust (Ps 91:1-2). There is no better resting place then the arms of our loving savior. God will give our souls a much need rest from all the foolishness and the mundanity of life, for He restoreth our souls (Ps. 23:3). Let us go to the Lord for rest; we will find Him to be very accommodating.