As someone who lives in the heart of Seattle and doesn't have my own car, I often take advantage of the city's public-transit options. Although our network of public transit isn't as extensive or sophisticated as that of New York City or Chicago, you'll be able to get around with relative ease, though be prepared for some hills if you're traveling on foot.
If you're planning to take public transit, I recommend using the Puget Sound Trip Planner to plan routes by bus, train, light rail, streetcar, ferry, water taxi, and the monorail. If you're visiting for just two or three days, you don't need to get a car, however if you're planning day trips outside the city for hiking or visits to nearby Vancouver or Portland, a car will be more convenient.
Here are the best options for getting to and around Seattle.