Either the Guildford Arms or the Halfway House.
To get to the Guildford, go up the steps to Princes Street cross the road and turn right. when you pass burger king turn left and the pub is at the top of the wee side street. It's a spectacular pub and something of a Cathedral to good beer.
To get to the halfway house, go out the back entrance to the station and cross the road to the fleshmarket steps, halfway up them is the halfway house (duh!). It's a small pub but pleasant enough.
Cheers!
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