This is an interesting question because so much depends on the situation. Was it infidelity, was it a loan not repaid--each situation is different and holds different weight. But, having said that, generally speaking, I think it is better for our hearts to forgive but not forget--because if we forget, it could happen again.
Say, in a situation of infidelity, eventually you can forgive, but it can be done while walking away--one does not have to stay and act as if it never happened. Forgive for your own heart, but walk away for your own sanity and well-being. One is not mutually exclusive of the other.