"Will you go out with me (to a place)?" is asking you to go somewhere. If a time is given, then you can assume it's a date. However, if it's simply, "Will you go out with me?", then he is asking you to be his girlfriend. I don't see a problem with you interpreting the question literally ("OK, where?"). A native English speaker may well respond the same way. :) You probably made the guy feel very shy - he didn't want to explain himself further.

Unless they are asking you to go somewhere, the most common thing they are asking is for you to date them/ to be their girlfriend.

If someone asks you "Will you go out with me?" They are asking you out on a date. Your reply of "Ok, where?" is the right answer. I do not understand why they would laugh and say never mind when you say "OK" unless they are really shy. I would ask them why they asked and then changed their minds. I think I'd be a little angry too.

When a person says will you go out with me they mean: 나랑 사귈래/요 In English, it usually means that (나랑 사귈래). It can also mean do you want to go somewhere, but this is a less common meaning. >~<