When I first started riding I got a book called Biking Puget Sound that has a lot of routes in it, and rates them by length and difficulty.
One of my favorite rides was a loop from Green Lake over to Golden Gardens, over to Gasworks via the Burke-Gilman, and back up the hill on Wallingford Ave. It was about 15 miles, and the hills were doable when I wasn't in the best of shape. Lots of great places to stop for coffee along the way. Plus, I could start from my place in Wallingford and GG was a perfect place to stop for a snack/water.
Here's the route (since it's a loop you can really start anywhere you like -- also, the book is more detailed, but this should give you a good idea:
Start at NE side of Green Lake, go west on Green Lake Dr N. Cross Aurora onto NW 83rd St.
At Greenwood Ave or 8th Ave NW, L then R to go west on NW 80th street.
NW 80th puts you on Golden Gardens Dr down to Golden Gardens Park.
Look for signs for B-G Trail coming out of the parking lot. Follow the trail S and E through Ballard and Fremont.
At Stone Way you can go right to go to Gasworks Parks or continue east on N. 34th Street and make a left to go up Wallingford Ave.
R then L at any time to get on Meridian, continuing north. Follow arterial back to east side of Green Lake to complete the loop.
2014 Bobbin Bramble / Brooks B67
2008 Rodriguez Rainier Mirage / Terry Butterfly Tri Gel
2007 Dahon Speed Pro TT / Biologic Velvet