I wonder if you can think of this in-between time as the social/emotional version of a big deep breath and a big long exhale.
I know that sounds a little cheesy, but bear with me here: know how when we do that with breathing, when we really take the time to stretch out that inhale and exhale, and really let ourselves feel the space it makes in our lungs, our whole bodies, even our heads? This time can be a lot like that: about making space for yourself and your heart and your head.
Like Sam suggested, can you use this time and space to focus on the parts of your life and yourself that may have gotten less attention or focus (or none at all), and regroup and reconnect with those? How about with a friend or two you probably fell out of touch with during your relationship with your ex, but would like to reconnect with? Or some new friends it sounds like you could make with your plans for that run? What about things you have wanted to try or do, but haven't yet gotten the chance to?
Sometimes one of the great things about having this kind of "time-between" is that you get a chance to re-assess and re-experience all of what you want in your life, and your day-to-day, so that if or when you start dating again, you go into it having a better sense of the place there is for it in your life, especially if you also a) want it to be healthy for you and b) want it to really add to your life, rather than be your whole life, or only really mesh with very limited parts of it, know what I mean?
I don't know about you, but I'm a big reader, and I also like to use times like these in my life to re-read a book or two that I have previously found very inspiring or influential, to kind of remind myself of who I am and what really matter to me: to get re-inspired about my own self and life.
Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has. - Margaret Mead