Edinburgh is a beautiful city to explore. Once in the city center you don't need a car to get around as it is very walkable. You can visit the Castle of Edinburgh or stroll shops and cafes on the Royal Mile.
At 820 feet, Arthur's Seat is the highest point in the 640-acre Holyrood Park. Also easy to climb are the dramatic Salisbury Crags, a series of 151-foot cliffs adjacent to Arthur's Seat. The easiest way up is from Dunsapie Loch, where there's a good-sized car park. Alternatively, you can walk from the Old Town, heading up past the Dynamic Earth science center onto a path that leads from Queen's Drive
The Palace of Holyroodhouse is the Queen's official Edinburgh residence and has frequently been at the center of Scottish history. Built in 1678, it was where James II and James IV were each married, where James V and Charles I were crowned, and where "Bonnie Prince Charlie" held court in 1745.
The nearest train station to Skye is in Kyle of Lochalsh, which is situated off the island, just before the Skye Bridge. To get there from Edinburgh you need to change trains at least once, in Inverness, and the quickest journey time is 6 ½ hours (although it can take up to eight hours if you don’t pick the right trains!). You can plan your journey at trainline.com. I would recommend planning to stay a night or two. You can also get there by car if that is your preference. *There are several tours that offer both Inverness and Isle of Skye. They would provide transport for you. Viator or Tripadvisor have a few options available.
It is about a 3.5 hour train ride from Edinburgh to Inverness. The fun of the train is the chance to travel across the famous Tay Rail Bridge, a mile-long feat of engineering constructed near Dundee in the late 1800s. The route also takes in the same great views of the Cairngorms. If you're planning on doing a lot of rail travel in Scotland, you may want to purchase a BritRail Spirit of Scotland Pass before you leave home. This handy pass will save you money, and allows you to hop on and off trains at your leisure. Even greater savings can be enjoyed if you're booking through ScotRail three months in advance, with fares shown for as little as £5 one way. You can also get there by car or bus depending on your preference.