Hello! PNW-er here. Born and raised in Vancouver, but moved to Portland last year after graduating college.
I haven't spent a lot of time in Seattle, as Portland is most likely less rainy, warmer, and has plenty for me to do. My recommendation would be to visit Portland, then Seattle.
The Portland Nursery in SE Portland is a nice little place. It's in my neighborhood, so I am partial
I hear the Chinese Gardens are interesting, but I believe they charge for admission.
There are also several rose gardens in the City of Roses... what a surprise. Washington Park (more famous) and Peninsula Park are a couple I have been to.
Any of the Mcmenimans restaurants are awesome for visiting, and good beer and burgers. Most of them are unique historical buildings, restored in Mcmenimans funky style. Kennedy School: (Kennedy School Movie Listings brought to you by McMenamins
) for one suggestion. There is even one that is Grateful Dead-themed (Barley Mill Pub).
Burgerville is my favorite locally-owned, sustainable fast-food chain. It's worth a try if you need something quick. They are spread around in Portland and Vancouver.
Mt. Tabor provides awesome views of Portland's city-scape, while being on top of an extinct, nature-filled volcano.
Forest Park is also pretty for walking.
The new Portland Boardwalk (The Eastbank Esplanade) along the Willamette River (the river that separates East and West sides of town) is also a nice walk, especially in the evening.
If you are limited to being in Vancouver, I would stay somewhere near downtown. There is more to do, though even then, still not much. If I ever had someone visiting from out of town, we always go to Portland, so I really can't think of anything to do in Vancouver. There is a small farmers market downtown on the weekends.
I can't offer much as far as Seattle recommendations. It's an amazing city as well, though.
You can take the Greyhound up to Seattle. No ferry needed. Just Interstate 5 all the way. You can get along with public transit in Portland, and as I understand, in Seattle as well. There is some public transit in Vancouver, but it's not as frequent.
Enjoy!!!! It's a wonderful, green place up here!!!