The Bucket Fountain
Right next to Iko Iko is Japan City, which I also feel has something for everyone but in a pencils-with-anime-hamsters-on way. There are some useful things here, but mostly it's strange little items that you want but don't need (they have a whole aisle of squishy keychains that look like baked goods). It's bizarre, but affordable and perfect for someone who likes weird things.
Stay tuned for a post on the Wellingon Night Market (coming soon to an electrical device near you).