The question needs to be split before it can be answered
"Where do crickets go in winter" sounds like one question with one answer, but it's actually two questions about two unrelated animals that happen to share a common name. One is the loud, chirping field cricket that fills a New Hampshire yard every September and then genuinely dies at frost. The other is a quiet, humpbacked jumper that lives in damp basements and crawlspaces and was never part of that outdoor cycle at all.
Which answer applies to you depends entirely on whether you're remembering a sound from last fall or looking at something moving across your basement floor right now.

