I would suggest Golden Gardens Park, in Ballard (neighborhood in North Seattle). It's a large beach park. If the weather is nice, you can have your ceremony on the beach for free, and if it is not good, you can hide under one of the bbq/picnic shelters.
You can officially reserve one of the shelters from the city of Seattle, but may not be necessary that time of year. They also have the "bathhouse" that people rent all the time for larger weddings, but probably wouldn't be necessary for your small ceremony.
After the ceremony, you can go to Ray's Boathouse just a few blocks down the street for continued great views, and get a nice dinner. Good seafood (or so I hear), and a few vegetarian options. If you go at happy hour, they have a decent happy hour menu. Make sure to reserve upstairs in the bar though.
Or stay at Golden Gardens and have a bonfire and bbq in one of the firepits! Ignore alcohol rule, and just pour your beers in a plastic cup. Some people don't even worry that much.
I hope you have great time in Seattle. Congratulations.