I have visited Edinburgh a few times during business trips, and I can assure you that 3 days will be enough. It’s a small city. I would check about tickets in advance for all the places and make sure to have that all sorted. I did the castle, the Royal Mile, whiskey tasting, the catacombs and visited a few cemeteries. Enjoy. PS Bring an umbrella and a rain jacket
Definitely go! It’s one of my fave places in the UK. I highly recommend trying a walking tour with a local, I signed up for a free one (and if you enjoy it, you can tip however much you like at the end) and it was amazing learning about all the history and stories of the old and new town. The whole city is more or less walkable. Just prioritize what sights you’d like to see and be weather-prepared. Some local things I tried: pies, porridge and honey for breakfast, shortbread ofc, Irn Bru and fried mars bar