There is not much in the way of sandy beaches in Seattle. However, there is a sweet little gem right on Puget Sound in a neighborhood north of downtown Seattle called Ballard. It's packed on the weekends with locals having BBQ or improv group picnics.
I like to go on the weekdays if I can, it's not too busy. Its a great spot to sit and people watch or gather your thoughts, or remember there is something bigger than you and your current set of circumstances. 30 minutes of your bare feet in the sand and the ocean in front of you, can bring some meaning and perspective to your hectic modern life, and it's right there 15 minutes from downtown and free.
Particulars: a concession stand operates most days during daylight hours. They serve "ice cream truck" type faire, as well as hot dogs, sodas and sports drinks. There is community room available for booking events. Restrooms near the concessions. Just south is Little Coney Island restaurant. fish and chips, burgers, soft serve ice cream and other fast food items. Restrooms and boat launch right next to the parking lot.
Little Coney Island is pricey in my opinion for what you get. If you want better Tasting and larger portion fish and chips. head back toward Ballard to the Loch Spot, sit down inside or enjoy the service windows and picnic tables in the back parking lot. Same food inside or out, one of the service windows has no longer popular soda's like "Green River" or "Big Red" and lots more... brands you may remember from your childhood, but haven't seen on store shelves for years. 
No booz outside though, so if you have to have the beer with your fish and chips...sit inside. It's a local hangout and you will definitely get the local culture if you decide to eat inside.

Fantastic place to kick it with friends and a big grill. Everyone drinks there, but be really careful of the police because even though they don't seem to personally care, they always write tickets for ANY containers of alcohol. During the day enjoy a big barbque and volleyball, in the evening hang out in drum circles with hippies (I'll be there, be sure to say hi) and big old rusty barrels that are used for bonfires. Definitely bring a musical instrument at night time! Yoga mat during the day.

One of my favorite places