Edinburgh - please help me choose which of these 2 hotels is best

Premier Inns are very consistent and I can’t see how you could go wrong with either location.

They're 20 minutes apart on foot. The Princess Street location is very close to Edinburgh Castle, while the Royal Mile location is (obviously) closer to the abusiness/noisiness of the Royal Mile. The Princess Street location is closer to Dean Village and Stockbridge, which is a much quieter but quaint neighborhood.

Will you be traveling to the hotel from Edinburgh Airport? If so, I would give the Princes Street location the edge, because the tram and the airport bus stop close by and it’s an easier walk with luggage. This is based purely on location; I haven’t stayed at either property.

We stayed at Premier Inn Edinburgh City Centre Royal Mile hotel and thoroughly enjoyed it. It’s not far from either the castle or Holyrood Palace. If going to HMY Britannia the bus stop is a few minutes walk away. The train station is across the street. I can’t speak for the other hotel.

There is also a Premier Inn at York Place (also on the tram line) and good for bus links. It's a quieter location that either of your other choices, but would be my preferred location.

I agree with Skyegirl about the Premier Inn on York Place. I loved this location as it was fairly close to the old city and the train station but is located in New Town, which has a much more residential feel to it. St. Andrew's Square was very close, and I loved walking up there with its beautiful trees and lovely buildings. Dishoom is located on the square and there are other restaurants very close by. I would definitely recommend this location.