Many of the higher traffic areas have been mentioned.
The Columbia Basin RR serves a large chunk of Central WA. Here is their service map. They run down to Connell weekdays, and maybe some weekends too, in order to exchange traffic with the BNSF turn that comes up from Pasco. Usually about Mid-Morning they meet in Connell.
If you don't already have one, an Altamont Press timetable for the region would be invaluable. Currently, I see that this one is the only one available. Maybe this is temporary, or they are phasing out of te timetable business.
Another timetable source:
Have a look at the online scanner feeds for the region. These will give you a good idea of traffic levels.
If you haven't found it, there is the grand-daddy of online Rail Photos.
Online railroad photo database, featuring over 749,000 high-quality photographs of trains, railroads, plus discussion forums, and more.
Some of the photos in my profile may have areas you are interested in, including the Oregon Trunk (Deschutes Sub).
Running east from Hinkle is the Union Pacific main line over the Blue Mountains. Plenty of traffic on that.
Many of the spun-off short-lines in WA are owned by the state of WA and their operations are contracted out.
The economic vitality of Washington state requires a strong rail system capable of providing its businesses, ports and farms with competitive access to national and international markets.
The St. Maries River RR is also a good looker. Their operations are local and scenic. Maybe others can fill in the blanks for their ops.
As the Port of Grays Harbor's operations have been expanded, so has the RR line servicing it. Should be a couple of trains per day, as the port handles grain and automobile exports. as well as a bio-fuel facility.
Since 1911, the Port of Grays Harbor has been providing the infrastructure and facilities for a diverse mix of businesses to prosper throughout Grays Harbor.