I like the "Greenmont" loop for a short ride. Up 24th, east on 75th to Greenwood, south on Greenwood, remain on it as it turns into Phinney, then you can either take Fremont, Stone, or Wallingford down to the Burke. From there you can take the Burke back, or head into downtown and ride back up along the Merytle Edwards (which can be just as crowded). Reverse that if you're starting in Fremont.
You can ride out to Golden Gardens.
You can ride up to Carkeek.
You can take the Burke over to the U District then take Lake Washington Blvd to Seward.
You can ride into downtown and take a ferry somewhere.
The best way to ride the Lake Washington loop, if you don't like the Burke, is to get the Burke portion out of the way first. Head out early and ride the loop clockwise.
Just riding into downtown is fun. I like to do it for the crumpets.
Really there's no excuse for driving somewhere just to go for a ride in Seattle, ever. Find an excuse to ride somewhere you've not ridden before and go there.
The best way of discovering what kinds of urban routes you like is to find a club/group/whatever you like and start going for rides with them. Cascade is the big one, I rather like Point83.