Paseo Caribbean Restaurant is ridiculously delicious, go for lunch to any of their locations.  The one in Ballard/Shilshole beach area is near the Ballard Locks and Golden Gardens Park, both cool places to check out.  Kerry Park has an awesome view of Seattle.  Alki Beach Park does as well.  You can drive or take a water taxi there.  On the same pier as the water taxi in West Seattle there is a great restaurant-Marination Station for a quick bite.  Some great hikes not too far from the city are Rattlesnake Ledge (not too difficult) and Mount Si (challenging).

In Seattle, I really enjoy the view at the top of the Volunteer Park Water Tower.

Within the city, there's a nice trail to the Discovery Park West Pt. Lighthouse. Carkeek Park has some nice trails, too. Outside of the city there are hundreds of amazing trails.

Take a ferry ride to Bainbridge or just over to Alki Beach Park in West Seattle.

There are many great restaurants in Seattle. I used to really like Black Bottle in Belltown (somewhat noisy, great bar), Agua Verde Cafe near University of Washington (excellent margaritas and tacos), Cafe Lago in Montlake (very nice italian food), and The Harvest Vine in Madison Valley (amazing Basque food).

A couple of my favorite places..

- The Pink Door - Italian restaurant in Post Alley (Pike Place) http://thepinkdoor.net

- Piroshky Piroshky - Russian Bakery in Pike Place http://www.piroshkybakery.com/contact.html

- Take the ferry to Bainbridge Island .. great for walk/hikes on a nice day http://www.wsdot.wa.gov/ferries/schedule/scheduledetail.aspx?departingterm=7&arrivingterm=3&roundtrip=true

I think Voodoo Doughnuts is a bit overhyped, but it's fun.  For a tastier pastry, hit up The Waffle Window (you can eat inside if it's not pretty out).  They have both sweet and savory waffles with amazing topping combos.

Nature-wise, you can hit Multnomah Falls - I think it's the biggest waterfall on the west coast.

Or hit Snoqualmie Falls near Seattle.

Seattle has awesome urban eateries.  If the weather is good, you could take the West Seattle Water Taxi to Marination Ma Kai (fusion hawaiian/korean food from the food truck voted best in the US).  Lola downtown has the best breakfast if you're downtown (grilled octopus for breakfast?  yes!).  You can wander around Pike Place Market for good nibbles, too.

If you get a nice day, wander around south lake union near the Center for Wooden Boats - pretty boats and some solid restaurants nearby.

In Seattle, we stayed at Inn at the Market and it was great, beautiful view, really helpful staff, and close to everything (including yummy cafes and bakeries) Pike Place Market is a must as is the underground walking tour. Great view from the Space Needle but skip the food there as it's pricey and not that great.