the borders area from edinburgh

A number of tour companies do parts of the Borders as a day trip. I am arriving in Dcotland on Sunday and have a Rabbies tour next week for a day trip to the Borders including Vindolandia. https://www.rabbies.com/en-gb/tours/scotland/from-edinburgh/day-tours
If you go to Viator or Get your Guide, you can search for ones that include your locations of interest. I think they include the company providing them and then you can book direct.

I took this tour last year and really enjoyed it:

https://www.rabbies.com/en-us/tour/hadrians-wall-roman-britain-the-scottish-borders-day-tour-from-edinburgh

The Borders covers a BIG so a lot depends on what you are wanting to do/see on a day tour.

Rabbies offers 3 one day tours from Edinburgh.

One of these may fit the bill. Depending on what you want to do, you may find you need to hire a car as public transprt around the Borders will limit what you can do and see - and there is a LOT! There are some attractive small towns - Melrose, Jedburgh, Peebles... There re ruined abbeys (Melrose, Jedburgh, Dryburgh, Kelso) lots of stately homes (Floors castle, Traquair House, Manderston, Mellerstain, Thirlstane...)

The Undiscovered Scotland website has ideas of driving tours - check out

https://www.undiscoveredscotland.co.uk/ustours/edinburgh-dunbar/index.html

https://www.undiscoveredscotland.co.uk/ustours/borderabbeys/index.html

https://www.undiscoveredscotland.co.uk/ustours/selkirk-langholm/index.html

Are you wanting to get into Northumberland with places like Berwick upon Tweed, Holy Island, Banburgh, Alnwick Castle etc? Again a car will make this easier.

We had a rental car when we visited the borders area and we were staying in Peebles. In addition to the Abbeys, we visited Selkirk to visit a woolen mill (Lochcarron of Scotland), Rosslyn Chapel, and Robert Smail's Printing Works (National Trust for Scotland). Prior to Peebles we were in Alnwick and visited its castle, Hadrian’s Wall, Bamburgh Castle and Holy Island.

I would not have wanted to reach the places we visited using public transportation, except Rosslyn chapel that is easy to reach by bus from Edinburgh.

I've done the Rabies one day tour to the Borders and Hadrians Wall. It was very good.

https://www.greattapestryofscotland.com/the-making-of-the-tapestry/

You could go by rail or bus from Edinburgh to see this.
Friends went, and said it was incredible.
The Borders area is lovely with gentle hills and pretty towns.

@SJ I have that as a planned diy day trip....suits my love of textiles.

Rosslyn Chapel is also an easy diy day trip from Edinburgh.