Hi! I studied abroad in Scotland for 2 years and it was amazing! I agree with Pamela. Pitlochry especially is such a nice little village to visit and is extremely easy to get to by train (and cheap). If you wish to go to an island, I recommend Isle of Mull (train to Oban and then ferry across to the island, check out the adorable, colorful town of Tobermory!) or take a train to Mallaig and then ferry to Isle of Skye. Isle of Mull is closer, and I did it as a (long) day trip to and from Glasgow. Both islands have bus transport on the island, however, depending in the season the times could be pretty infrequent.
If you want longer trips, going up north to Inverness is also very accessible via train and has a lots of nature to view along the way.
You can take tours from Edinburgh or Glasgow, however, you can often get to the nature-y places and have more time to hike or look around if you go on your own (and for cheaper). I also recommend trying a whisky distillery tour (or two, or three...). They are in almost every town.