It's about 400 metres to walk from Teviot to Budget Backpackers following these instructions, or about 600 metres to walk from Teviot to the Cowgate Tourist Hostel. You could also take a slightly shorter route directly to the Cowgate Tourist Hotel.
Head out of Teviot and across Bristo Square
Cross the road and walk down Bristo Place
Cross the road and walk down Candlemaker Row
You're there!
To continue to the Cowgate Tourist Hostel, carry on round the corner
Walk under the bridge
And you're there!