If you are driving, you can take the A68 road which connects Edinburgh and Jedburgh. From there, you can take the A698 road to Coldstream. Another option is to take the A697 road from Morpeth, which passes through Coldstream on its way to Edinburgh.
If you are traveling by train, the nearest station to Coldstream is Berwick-upon-Tweed. From Berwick-upon-Tweed, you can hire a taxi or take a bus to reach Coldstream.
If you are coming from Edinburgh, you can take the train from Waverley station to Berwick-upon-Tweed, which takes about an hour. If you are coming from Newcastle, you can take the train from Newcastle Central station to Berwick-upon-Tweed, which takes about 45 minutes.
If you are driving from nearby towns, such as Kelso or Eyemouth, you can take the A698 or A6105 roads to reach Coldstream.
Overall, the best way to get to Coldstream depends on your starting location and preferences. Driving is convenient if you have a car, but taking the train can be a relaxing and scenic option.