Day trips from Edinburgh

Nothing related to tour companies, but if you want something to see, consider taking the bus to Rosslyn chapel (as seen in the Da Vinci code). It has ties to the Knights Templar and an interesting history. If i remember correctly, the bus will take about 40 minutes to get there. If you like castles, you can take a bus to Craigmillar castle (about a 30 minute bus ride).

Stirling Castle is a great visit, even though it might seem highly similar to Edinburgh Castle. You don't need a tour though, very easy to visit on the train and a short walk to the castle.

I second the Rosslyn Chapel recommendation. Depending where your Edinburgh starting point is, the bus takes 45 min to an hour each way. If you buy a bus day pass, you can use the bus again to go out for dinner or whatever after you return to Edinburgh in the afternoon.

At Rosslyn Chapel there are free talks included in the entry fee, so you don't need a tour guide of your own. There's a well-equipped visitor centre with a cafe, gift shop, and some interactive exhibits.

Is this a first visit to Edinburgh? You could very easily fill up those days with in-town items vs. going out of town, especially with just four nights. But, I can recommend you browse the day tours from https://www.rabbies.com/en/scotland-tours/from-edinburgh/day-tours .. wow, they even have an in-town tour available now .. I'll have to consider that for next trip .. whenever I am so lucky to go again.

One thing to remember with day tours is the distance. I did a day trip to Hadrian's Wall with https://www.heartofscotlandtours.co.uk/ (was back in 2008) and I remember some voices complaining just a bit about the relative shortness of the time once there, but it was a long(!) way to get there versus a hop/skip up to St. Andrews with Rabbies (we had several hours to explore on our own once there).

You can also do self day trips with regular public transport .. the noted above Rosslyn Chapel and Stirling Castle are two possibilities. I used the bus to get to the National Museum of Flight http://www.nms.ac.uk/national-museum-of-flight/ and a visit to ride the Falkirk Wheel was done using the train https://www.scottishcanals.co.uk/falkirk-wheel/ If you have kids, I think the Flight Museum was more fun as a day's outing. The canal boat ride was fun, but not too involved an activity.

There is probably enough in the capital for the time.

If you want to go further, get a map. Draw 80 km from the Palace. That is the best day trip distance. It includes Dundee and Glasgow.