Late October in the WA mountains – it could be fine weather, but pretty good chance of lots of rain and snow that time of year too. Each year is different – last year we had no Fall at all (winter began after September). Year before that was great, snow-free hiking into mid October. I’ve also seen 2 feet of snow in early October – it’s a crap shoot that time of year. Best to make conservative plans, be willing to change or adapt plans as needed at the last minute, and have appropriate shoulder season gear and cold weather skills to deal with extended cool, wet and maybe snowy conditions.
One approach would be two or three shorter backpack trips or some nice day hikes. If the forecast looks good, then have a plan for a longer trip if you want to roll the weather dice. If forecast looks cold and wet, then shorter and/or lower altitudes are a good option, such as the Olympic coast (day hike or short overnighter), or hikes in the rain forest or lower altitude valleys. If there is not much snow pack yet, and the forecast looks good, then you have more options in the higher mountains too.
Re: food caching – check with the land manager (call the local National Forest office, National Park, etc) you want to visit, but usually that’s a no-no. Either carry your food for the trip or arrange shipping a resupply package. Some areas require bear canisters as well (like the Olympic Coast), so be sure to check with the land manager in question.
There are LOTS of excellent and varied hiking and backpacking options in WA to choose from. You could pick one area and pretty much find whatever type of hike the weather, your skills and your preferences allow. Mt. Rainier NP is one example (long backpacks to short day hikes of varying altitudes). Olympic National Park is another example (coastal hikes, low forest valleys, high alpine ridges if the roads are open, etc, etc).