Berwick-upon-Tweed is directly on the East Coast Main Line, with fast trains from London King's Cross (around 3.5 hours), Edinburgh Waverley (under an hour), and Newcastle (40 minutes). The station is a ten-minute walk from the town centre. This is by far the most pleasant way to arrive, and the approach over the Royal Border Bridge is itself a spectacle.
By road, Berwick is on the A1 in Northumberland, about 50 miles south of Edinburgh and 65 miles north of Newcastle. The town has reasonable car parking. The nearest airport is Newcastle International, about an hour by car or train.