Lots of good suggestions have been made. Discovery park in Seattle and Point Defiance Park in Tacoma are a couple more great spots.
I am a portrait and wedding photographer and I encourage couples to personalize their engagement portraits by selecting a location that reflects their relationship and interests. Where you met, your first date, first kiss, where you proposed, or other memorable occassion, your favorite spot to hang out, or where you do your favorite hobbies. Ultimately, the portraits should be about the two of you more than the location.
Have you booked your wedding photographer? The engagement session is a great opportunity to get to know and work with your photographer in a relaxed setting before the wedding. Also many offer a special engagement package to their wedding couples. Your photographer should have ideas for you if they are experienced.