You've missed something, I don't remember the exact spot but there is a door somewhere on the eastern side.
Re-ni-AN-nen - strayed (ppt. of renia- 'to stray')
Aeled Reniannen, Defender of Middle-earth ~ Nendhiniel, Forge-Warden : Captain and Wardenette from [EN-RP] Laurelin
Fluffrash, Blade of Barashish ~ Nathraen, Conqueror of Towers : Warg Puppy and Spider Tailor from the darker side thereof
Faradwen, Swift-Arrow : Huntress from [EN-RE] Landroval
As if in answer there came from far away another note. Horns, horns, horns. In dark Mindolluin's sides they dimly echoed. Great horns of the North wildly blowing. Rohan had come at last.
Kári was a little Dwarf. / Smaller than you or me. / And wherever Kári went / He took his axe… or three.
To get up to that door, first go up the stairs were the vendors are. Then to the left and up the stairs and then go right up the next set of stairs. Keep following that path until you find a turn to your right. At that point you should see a door.
I hope that was helpful.
The doors really serve no purpose. It's just fun to find secrets.