It's even worse if you're heading to the Southside, as you either have to walk half of Prices Street away from where you're going, or climb up Fleshmarket Close/Cockburn street, which isn't a walk in the park even for the able bodied! A lift into North Bridge would do wonders!
To the left of Fleshmarket Close and the Scotsman steps is an entrance to the Carlton Hotel. Straight up in the lift and out the door to North Bridge

Now it's a Hilton they may be a bit more security alert though.