I know many people are all about the day trips, but I'm thinking if I had 3 days, I'd want to stay in Edinburgh and not even try to cover much of the city. (I say 3 days because it would be 3 full days. 4 nights, 3 full days, a half day on either side, which I'm well aware would be mostly settling in and packing out).
Having not been on the ground there, I'm appreciative of anyone who has a feel for things and can suggest what a non-rushed itinerary might include. We are very open to off-the-beaten-path or more low-key things. I do research and read blogs, but I find fellow travelers to be very thoughtful and appreciate the insights.