Hurricane Ridge is ALL that you will be able to see...you will not be able to see ANY of the park. Travel time will eat up your day, and days are getting shorter at the end of October. The attractions that most people come to ONP to see are from Lake Crescent west to the coast and then south. Considering that weather is so changeable in the HR area you may be making a long drive for nothing.
This is the webcam view today...check the webcam before you leave Tacoma.
I feel exactly the same way as Bobmrg. I hope, at least, that your trip would be on a weekend, as the traffic between Port Angeles and Tacoma is ghastly in general but even ghastlier on weekdays. Late October is usually a time of rain and fog, which could make a visit to Hurricane Ridge unpleasant and even dangerous. The days are fairly short, too.
Watch the weather forecast. Driving all the way to Hurricane Ridge is not worth it if it is socked in, which is very typical in late October. I am assuming that you have been to Mt. Rainier before? If not and the weather was decent IMO that would be a far better option. An option if it were grey would be to visit the Eastern Side of the Olympics and visit an Old Growth Forest. One option would be Staircase near Lake Cushman.