I’m excited to hear that someone else is still trying to get out backpacking in November!
As previously mentioned, where you go will greatly depend on your winter backpacking experience. If you are comfortable snowshoeing this will open several trails that would otherwise be inaccessible. If snow is in your plans; Please be sure to check the Northwest Avalanche Center website for snow and avalanche forecasts.
We have an article called Top Picks for Winter Camping in Washington. Most of the article discusses campsites you drive to, but the last 4 mentioned are for backcountry snow camping. I have been to 2 of the 4 locations listed. They are beautiful overnight trips that can be turned into multiple nights for further exploration.
If you want to avoid snow, then sticking to lower elevations will be your best bet. Dave mentioned Shi Shi Beach & Cape Alava Loop. I love this hike, but please note that the Shi Shi Beach trailhead is currently closed. The trail is located on Makah Tribe land and has been closed to the general public until further notice. It may be open by the time you are preparing for your trip. Here is the link to the Makah Tribe Public Announcement with the most up to date information.
Lake Cushman & Staircase area of Olympics are also inaccessible due to Forest Road 24 closure.
Further details with updates on the closures within Olympic National Park can be found here.
Greenwater and Echo Lakes is another low elevation hike that can be done in 1-4 nights. Greenwater Lakes Trail can be taken to Echo Lake, Lost Lake, Noble Knob, or Hidden Lake. Depending on the weather and the distance you are comfortable hiking a loop (aprox. 25 mi) can be made connecting them all.
Wherever you go, I hope you have a great time!