After dropping your bags at the Hawthorne Hostel, spend an hour or two wandering the Hawthorne shopping area, exploring vintage thrift stores, browsing books at the Powell's branch, and doing some serious people watching.
When you get hungry for brunch, check out the Waffle Window's ridiculously gourmet but cheap waffles. Then head to Kruger's Farm Market - one of the many farmers' markets in Portland, located on Hawthorne and 23rd and open year-round where the snack options are fresh and local.
From there, grab a TriMet bus back across the river and ride the MAX up into the hills of Forest Park for a hike and picnic. Start out at the Hoyt Arboretum where you can see a vast array of tree and plant species and then branch out into as long a hike as you would like.
If it gets rainy, ride the MAX back into downtown and spend the afternoon exploring Powell's City of Books (where you can take un-purchased books into the attached coffee shop and read until you decide which one you have to buy).
For a quiet evening, take the bus back to Hawthorne and catch a movie with pizza and beer during happy hour at the Bagdad Theater and Pub.
For a more adventurous night, take a bus to the North Portland gayborhood and walk out to the Skidmore Bluffs, where you'll get beautiful views of the sunset, the North Portland industrial area, and a diverse crowd of punks and queers also enjoying the popular spot.
From there, grab some of Portland's best bar food at the Florida Room, and then head across the street to In Other Words Feminist Community Center for Dirty Queer, an X-rated queer open mic full of erotic poetry, stories and music and packed with locals (entry by donation). If you miss the Dirty Queer night, check out whatever rad event is happening at In Other Words.
The bus ride back to your hostel may be a little long, but you'll have plenty to think about on the way back.