I often walk along Queen Anne's "boulevard", which includes Kerry Park and other wonderful views. Sometimes, I include a stop at Macrina either before or after - ginger apple cider really warms you up. This route is really popular, so you will get that "safety in numbers" feeling from all the runners, baby strollers, dog walkers, and others.
Here is a description of the route:
The Seattle Parks website is a good place to look for other ideas too.