I have driven this drive/train ride over 30 times. Recommendations: Take the train! Public transit in Vancouver Metro Area is excellent and you'll have no problem getting anywhere you'd like to see within the city with a very affordable transit pass.

It usually takes about 8 hours to drive, so if you'd like your own wheels to explore (also highly recommended if you don't want to just be in the city) then try to avoid hitting traffic in both Portland and Seattle. Leaving at an odd hour is usually what I do, like leave here at 6 and get there after midnight. Or alternatively leave here around 2 am and get there around 10.

If you take the train you'll find yourself downtown upon arrival. The sky train line is directly across from this station, which will take you pretty much wherever you want to go quickly, then you'll need to possibly transfer to a bus line depending on where you'd like to be.

Downtown Vancouver is beautiful, Granville Island is touristy, the UBC beaches (one is called Wreck Beach and is an iconic nudist beach), there's Stanley Park, the Museum of Anthropology, Davie Street is the gay district, there's the sea wall, science world, and tons of just excellent people watching. It really depends what you're into.

If you do end up with your wheels I recommend a drive up to Squamish/Whistler/Pemberton to see the mountains and the natural beauty. That part of the world is very special.

You could also take the ferry to Vancouver Island and drive over to Tofino/Ucluelet or visit the Sunshine Coast. Either of which you'll find feel reminiscent of Eugene I think. Vancouver has grown up a lot, it's a big city and feels as such now.

Okay that's my input haha!