A well-reviewed city such as Edinburgh hardly needs additional adverts, so I will primarily add my voice to the general admiration that it produces from everyone who visits. I've been to Edinburgh several times over the last decade, most recently in March 2023, and my affection for it grows with each visit.
Despite its hilly topology, Edinburgh is a very walkable town, and major monuments and points of interest are practically all within walking distance from each other. Soaring monuments and church spires pop up in perspectives every few hundred steps or so. Sweeping panoramas open up from places such as the walls of the Castle, Calton Hill, Arthur's Seat (one single point of interest that requires a true hike to get to), or from rooftop terraces such as the one at the National Museum of Scotland. The numerous closes around the Royal Mile are the opposite of wide-open spaces and quite fun to walk through and linger at - hardly anything else anywhere gives you a similar feeling of seeing the "insides" of the city.
The color palette of Edinburgh's Old Town is rather muted, even on the sunniest of days, despite many architectural standouts throughout the town. Nonetheless, splashes of color are found in many quarters, most notably on Victoria Street or Cockburn Street. The New Town is brighter by design, with plenty of architectural standouts of its own.
Of the main attractions, Holyroodhouse Palace and Edinburgh Castle are each worth a visit. If you like including art, culture, and history museums in your itineraries, several of the main ones in the city are free (e.g., the National Gallery or the National Museum). Churches such as St Giles' Cathedral or Greyfriars should also not be missed. You can technically see all of Edinburgh's core zone in about a day. Stretching it to at least two is the minimum I would recommend.