It would help to know if you are planning to rent a car or use public transportation, and also if you plan on visiting in the summer or off-season. It would also really help to know what your interests are besides hiking. And by hiking, do you mean gentle walks, or hardcore 8+ mile hikes?
That said, I would second wasleys' recommendation for Arran or Mull, but especially Arran. The island is very easy to get to and has the added benefit of being less crowded than Skye, which can really pack the tourists in during the summer. And it's small enough that you could easily see everything in the time you have. To get to Arran, you just head to the Ardrossan ferry (about an hour west of Glasgow), and take the ferry over to Arran (about 30 minutes). You could take the train from Edinburgh to Glasgow, then pick up a car outside of Glasgow, or if you're not renting a car, take the train to the ferry and then ferry over on foot. It's a small island so you could see a lot in a few days, especially if you're renting a car; but it is easy to get to and get around using public transportation, if you wanted to forego the car. Arran has a very good bus system that can take you most places.
At any rate, the scenery on Arran is beautiful and it is not called "Scotland in miniature" for nothing. https://www.visitarran.com/ There is wonderful hiking, mountains, beaches, Brodick Castle and gardens, the Lochranza ruins, ancient cairns, quaint fishing towns, and several whisky distilleries. I loved Arran Aromatics, a shop that has wonderful bath and body items that are made on Arran. I had to tear myself away from there. :-) I was in Scotland for 3 1/2 weeks in May of 2023 for 3 nights and loved my stay.
I also loved Mull, which is a beautiful island. Tobermory is a delight to stay in, and seeing places like the tiny island of Iona, Duart Castle, and Calgary beach was wonderful. Don't get me wrong; Skye is pretty wonderful, too, but given the crowds, I preferred Mull and Arran. Skye also has pretty limited public transportation, which makes it difficult to get to some (many) of the main attractions. It can be done, but it takes time, and research. So if you are not renting a car, it's definitely something to think about.
One thing Skye has going for it, though, is the Isle of Raasay, a sort of "wild" tiny island that is about a 10 minute ferry ride from Skye, and is an incredible place to visit. Not too many people go there, so you can do a lot of things without crowds. It has Raasay House, which is a hotel, which I have not stayed at, but hope to one day, and also a lovely cafe where you can enjoy lunch or afternoon tea. And there is a very nice distillery there as well. I enjoyed the distillery very much, and the whiskey I had was wonderful. But most of it is remote beautiful scenery, some very old ruins, and Calum's Road, a 2 mile road built by one man over a 10-year period.
Or if you feel like getting a bit further from civilization, there are the outer Hebrides, like Lewis and Harris, which has beautiful beaches, the Calainish Standing stones, which are older than Stonehenge, Lews Castle, and much more. I saw much fewer tourists there, and enjoyed my time very much.
