I stayed at the Premier Inn on York Place and found it quite satisfying. Good location and reasonable price. A couple of people here have stayed at the Ibis on St. Andrew Square, and rated that high as well. I like that area (New Town) better than the Old Town, as it is less crowded and has a more residential feel. But in terms of your selection, the Ibis is usually pretty consistent in terms of quality.
I was not crazy about Edinburgh Castle - I liked the outside of it, and the view from up there is wonderful, but I would not go back to see it, especially for the high price. But others here really enjoyed it so YMMV.
I loved St. Giles Cathedral. It is quite beautiful and has so much history. Make sure you go outside so you can see parking space number 23, which is where John Knox is buried. 😊 Seriously.
The National Gallery is nice and I enjoyed it but I would strongly suggest visiting the National Museum of Scotland, which is absolutely amazing! I loved that museum and there were so many incredible things to see there. Definitely a must see in my opinion. Greyfriars cemetery is also very interesting. There is a small pub near there called Sandy's where you can listen to some local music.
I did not make it to Holyrood Palace as it was closed the week I was there. I would suggest checking the website before you go because it does seem to shut down for periods depending on what's going on. I also did not get to Holyrood Park but did make the climb up Calton Hill to see the Nelson Monument and the other buildings up there. Beautiful view and very easy to get to.