Why do you want to date a runner? If you are a fast man, she will not be able to keep up with you, so you won't actually run together. You may not have the same goal distances - let's say she's very fast and serious about 1500 m / 5K; you won't have the same goal races. (And you'll want her support at your goal race if you're targeting an OTQ anyway and vice versa.)
Two out of the three men I seriously dated, including my now-husband, took up running or began running again due to my influence. My husband started running again when we were dating and has been running ~1300 mi / year for 15 years+ now, and is more serious about running than I am at this point (mostly because my IT band hates me.) But we never run together. Why not? We have three kids, and unless we want to push our 4-year-old in the stroller (we don't) it's not happening. Just too much trouble.
I don't think it's important to date a runner.
But I DO think that both being athletically inclined has been hugely important for our marriage. We can do things together that require being fit, like hiking, skiing, cycling, snowshoeing, etc. We both take care of our bodies. I like being married to someone who is fit and looks it. We value eating relatively healthy. We like to be active in our free time, not just veg in front of the TV (though we do that sometimes, too.) I think it's a mindset, and that active / healthy mindset is what you should be looking for, not specifically a competitive runner.