Robbie's bar is the good pub on leith walk, but no good for bikes.
I haven't been in any of the Rose street pubs for many years so could not say what they are like but there are racks
Kay's bar remains the best pub in Edinburgh but is most definitely one to walk to. Pubs and walking is something I like to combine.
There are racks near the grey horse in Balerno but the pub is better after dark with the fire going which is hardly conducive to cycling.
There is a pub near the forth and Clyde canal I had a couple of good pints in on a day out to the Falkirk wheel. You can get liquor in the wheel cafe but that is not a pub. But come off the union canal and head along the forth and Clyde wee bit. I am afraid I cannot remember its name.