If your looking for a one-day hike that gets up into the alpine area, I would recommend the Putvin Trail along the headwaters of the Hamma Hamma. It's only about 3.5 miles in, but it's steep, very steep, and you should be in good condition to do this one. The trail goes up to Lake of the Angels, which is one of the prettiest lakes in the Olympics, and late September, when the huckleberries turn red, it's a magnificant scene. I've taken several groups of people of there in the last few years, and after they stop remarking about the severity of the climb, and get to the final terrace, they are happy campers indeed.
You should be able to locate this trail in any of the hiking books about the Olympics.