"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.