If you're staying in Seattle, the ferry from downtown by the Seattle Aquarium goes to Bainbridge Island. It's a cute artistic town with tons to do right off the dock. If you're staying near Bothell, the ferry in Edmonds goes to Kingston which also has a lot to do right off the docks. In Mukilteo there's another ferry that goes to Whidbey Island. They're about 30ish minutes each way. You can walk on or drive your car on. Just know, they're serious when they say to arrive 45 minutes early if you plan on driving your car.
There are tons of whale watching in the Puget Sound from Seattle to Canada. This one has a spot in Edmonds which is about 30 minutes from the venue. You can often see them during ferry rides, but you can go on tours where they go to where the whales are! It's such a cool experience so you should totally try it if you have time!
If you're not feeling adventurous and would prefer to relax with a nice glass of wine, check out some of the wineries near Woodinville! Chateau ste Michelle is a big one, but there are tons of smaller ones for wine tasting.
You can spend a whole day on one block! The Space Needle, Chihuly Glass Museum and the Museum of Pop Culture are right next to each other! All of this is close to downtown and the water. Museum of Pop Culture has tons of cool props from your favorite tv shows and movies, as well as a whole floor dedicated to musicians from Elvis, Soundgarden, imi Hendrix and more!
They recently finished construction on a new walkway that goes from the Seattle Great Wheel past the aquarium and to Pike Place. You'll walk along the water looking at the mountains and there's tons of spots to sit and have a cup of coffee, places to eat and shop.