My advice would be to assess whether or not you would take the job if she didn't exist. If it's something that you want to do then you shouldn't let the awkwardness of having an ex in the same city stop you. If you were only doing it to stay with her and the job itself isn't that important then I would strongly suggest that you either stay in your current city or go somewhere else. In this situation your first priority has to be yourself and you should really do whatever is best for you.