I'm sorry, but how is a cosplay not a costume? Cosplay = costume play. Wearing cosplay pieces is fine, I've worn my Athena/Anri pleated skirt out because it's a fine and dandy skirt. But I wouldn't wear my full costume out, I'd look dumb walking around in a sailor uniform.
Wearing regular clothing with a wig isn't something I consider cosplay either, I was going to possibly wear a blonde wig and regular clothes, it's not like people will think I'm some weirdo for having blonde hair.