Welcome Ben it shouldn't too hard for you to get a job with experience. The largest hospitals are Legacy Emanuel, Oregon Health Sciences University and Providence St. Vincent. There is also Legacy Health's Salmon Creek in Vancouver, Legacy Good Samaritan (smaller).
On the East side there is Kaiser Permanente Sunnyside. I hear Kaiser has great benefits for employees.
For new grads there are zero jobs, but if you have a little experience, there are plenty of jobs. You may want to skip traveling and just try applying for some positions. You shouldn't have a problem landing one.
The Wilsonville-West Linn (just south of Portland) school district is one of the top rated in the metro area.