I too suggest some space, not to try jump into being best friends right away. My ex is just about my best friend, but after we broke up he did a lot of traveling and was in and out of town, so we had intermittent contact for a few months. I think regular breaks from spending too much time together helped a lot with our friendship being able to continue. It's important to have the space to be able to think clearly and make sure you don't continue poor relationship dynamics just out of habit.
Happiness will never come to those who fail to appreciate what they already have.