Even though "I didn't go... yet" has many more google results than "I haven't gone.. yet", the "didn't go" results are mainly from blogs and tweets. By switching the search to news articles, suddenly "haven't gone" is much more common... much, much more. My thought is to follow the standard rule: "I haven't gone/decided yet" (because we are talking about now, so we use present perfect). Although "didn't go/decide" is in common use, it would likely look like you've made a mistake. Only use that with people who already use that kind of phrasing. Until then, there's nothing wrong with using the standard "haven't gone/decided".

When you use yet, haven't sounds more natural to me. When you use didn't it seems to be be more finalised. The sentences below seem natural. I haven't decided yet. I haven't gone to bed yet. By 2 pm I still hadn't gone to bed. I didn't go to bed until 3 pm I didn't make a decision yesterday