Are there any good whiskey distilleries that I can visit on a day trip from Edinburgh without a car?
you could take a day trip to Pitlochry, about 2 hours by train from Edinburgh, lovely place ,winners od Scotland in Bloom on several occasions. 2 distilleries there ,Blair Atholl in the town itself maybe an 5-10 minute walk from the train station,then there is the Edradour Distillery about a mile or so outside the town,you could walk or take a local taxi to there. both are excellent places and do good tours.
The Town of Pitlochry is really nice and has a dam with a very famous fish ladder,you can walk across the dam and down by the fish ladder. there is also a Heather gem factory.
and just outside the town is an old inn with its own micro-brewery.
I once had venison stroganoff in there which was superb.
Dalwhinnie distillery is near the Dalwhinnie station on the Highland Main Line. Dalwhinnie was our favorite whisky of those we sampled. I would have loved to stop at the distillery -- the scenery is awesome -- but we didn't have the time. Here is the train schedule https://www.thetrainline.com/train-times/edinburgh-waverley-to-dalwhinnie