How long are you going to be in Edinburgh? There is a lot to see there and if you are only going to be there a few days, you may not have time for a day trip. When I was there, I spent a half day the Holyrood park and Arthur's seat, a full day with the hop on/hop off tour and did the castle and used the bus to get to the Britannia, Then I spent a full day walking the city, royal mile. And I felt like I could have had more time.
I think an easy day trip would be Stirling Castle of William Wallace fame. You could drive it or take one of the tours. St. Andrews and Glasgow are also both a good day trip distance by train.
I did a full day tour through Greyline tours where we drove through some of the Highlands and up to Loch Ness. The sites were beautiful but I would not recommend doing something like that. It is too much ground to cover and we spent most of the time in the bus. I think if you really want to appreciate that part of Scotland, you need to devote several days.
Funny enough, I asked this same question about ideas for day trips from Edinburgh last spring and I received several eat ideas. I will try and find the post and give you the link.