I'm planning a playthrough doing exactly this. Does anyone have any good ideas for stuff I could do?
Obviously the character will level a bit, because you'll still level speech by selling/buying stuff, get skill points as quest rewards, but this can be kept to a minimum.
There are lots of 'skills' in Skyrim that don't level your character. This includes:
-Unarmed
-Unarmored (mage armor doesn't really count)
-Shouts
-Cooking
-Lycantrophy
-Vampirism
-Use of staffs and scrolls
-Misc. crafting stations like the atronach forge or imbuing chamber
-Powers like the all-maker stones or black book powers
So my character would be a clothes-wearing dragonborn werewolf khajiit master chef (not a fan of vampirism) carrying around lots of staffs and scrolls, and using lots of powers. I'll probably use gloves of the pugilist as the only armor piece, which shouldn't level light armor too much.
Does anyone have any additions? Any advice?