Cobram is on the Murray Valley Highway on the Victorian side of the river, about 240 km north of Melbourne — around three hours by road via the Hume Highway and Shepparton. From Sydney it's about seven hours via Wagga Wagga.
There is no longer a passenger rail service; the line closed in 1993. The nearest stations are at Shepparton (an hour south) with V/Line trains to Melbourne, or Yarrawonga (45 minutes east) on a different line.
By bus, V/Line runs daily coaches from Shepparton via Numurkah. Most visitors arrive by car — the highways are good and parking is never an issue.