Drop your bags at the Green Tortoise hostel and head to Pike Place Market (the oldest, continually running farmer's market in the USA), which is just a short hike up the alley from your hostel room.
Buy fresh, local produce for a budget friendly picnic in the Olympic Sculpture Park and take a downtown bus to the Gay district, Capitol Hill.
Grab a craft coffee from Analog Coffee; walk to Cal Anderson Park and sprawl in the sun. Watch the various sports games and their corresponding LGBT players do sporty things.
If it is raining (it will likely be raining), stroll down Broadway and duck into the vintage, thrift, and otherwise upcycled clothing stores, especially Crossroads on Broadway. Slip into your new black, skinny jeans and sleeveless Riot Grrrl t-shirt and hand the cashier a cool $20 for your new, Seattle appropriate attire.
Head to Raven or Rudy's for a $30, drop-in hipster haircut - the best souvenir and only one that always fits in your luggage.
Happy Hour at Poppy is a great way to fill your belly for dinner and sample the craft spirits that make the northwest famous - happy hour is usually weekdays 5-7.
Catch a free summer night outdoor movie or bus over to Volunteer Park where the conservatory is free during the day and in the evening you can climb to the top of the water tower for amazing views of the sunset over Seattle's world famous skyline.
Head to Purr for some of the stronger well drinks in town and friendly gay-boy atmosphere. Grab a bus back to your hostel ($2.50).