Is there a site where open discussion subjective questions are accepted?
Well, first, I think this question would belong in a meta se, but also I don't think you are looking for a stack exchange at all. My impression is that the point is to ask and answer questions that a lot of people could have so that people can find those answers here. Discussion of the sort I think you are referring to I don't think really fits on any SE (At least, that is the impression I get)
You might try checking out one of the chat rooms, they are better for dicussing things.
That depends on what's being discussed. If you feel that your question meets a significant number of the guidelines for great subjective questions, and it's otherwise on-topic for the site (no career advice questions, or best coffee blend for programming, for example), then you might consider Programmers.
Walk through the FAQ, and the site's front page, to get a feel for what's acceptable. Note that it's certainly possible that there's no appropriate site for your question on the SE network. Some discussions are better suited for more traditional forums.