Odunpazari is picturesque and should be on your visit regardless of world heritage status. My fav is obviously the pink corner shop. The small alleys with colorful wooden houses and handicrafts are tourist gold. It's not unique enough on its own but I believe with the intangible culture and the mosque (I didn't visit) complex it will somehow get inscribed for enough niches.

Be aware that parking in high season must be quite hellish as it was already hard to find a good legal spot in January. At least it didn't snow in this part of Turkey then.