Kelso has no railway station — the line closed in 1964 — and the most practical approach is by car. From Edinburgh it is about 45 miles and an hour's drive via the A68 south to St Boswells and then east on the A699. From Newcastle it is a similar distance, about 50 miles, via the A697 north through Cornhill-on-Tweed.
Buses run from Edinburgh and Berwick-upon-Tweed via First Borders (route 67) and Perryman's Buses, but services are infrequent and take considerably longer than driving. The town is well placed as a base for exploring the other Borders abbeys: Melrose is 12 miles west, Jedburgh 12 miles south, Dryburgh 10 miles west. All are manageable as day trips by car.