Trail of the Shadows is the short walk that explains why Longmire mattered before Mount Rainier became a national-park icon. The loop passes forest, meadow, mineral springs, and traces of the early resort era, when visitors came as much for water cures as for mountain scenery.
It is flat, quick, and useful even if you are not planning a major hike. Do it before Rampart Ridge or after visiting the Longmire Museum; the interpretive signs give the surrounding buildings and landscape more meaning.