It is easy to spend a fun and exciting day in Seattle without a car.  There are lots of ways to modify this itinerary. Add a ferry ride from the waterfront. Spending the day at the Seattle Center or at the aquarium could easily extend this from one to several days. Take the Underground Tour in Pioneer Square. Visit the Klondike Gold Rush Museum which is fun and free.  In the summer months you can ride the passenger-only Water Taxi from the waterfront to West Seattle and Alki Beach.

Here's a sample one day itinerary:

Start at the Space Needle by taking the Seattle Monorail from downtown. Look around the Seattle Center or go to the Space Needle. If you're interested in music the EMP-SFM (Experience Music Project - Science Fiction Musuem) is located at the foot of the Space Needle.  It has a lot of rock'n roll memorabilia that you may find interesting.  The Chihuly Garden and Glass musuem is near the Space Needle and you can get a combination ticket for both.  It gets really good reviews.  If you're interested, then the Bill & Melinda Gates Foundation is across from the EMP and has a visitors center that is free.  Come see how Bill Gates is giving away his millions. 

Take the Monorail back downtown.  You will be at 5th and Pine (Westlake Center). Head west to the Pike Place Market. Look around then head for the Pike Place hill climb which is a series of steps that walk down to the waterfront.

You will end up across the street from the Seattle Aquarium. Plenty of things to do on the waterfront, boat cruises, seafood restaurants, the Aquarium, or your typical tourist activities. You can walk or take the waterfront "trolley" bus.  A cheap and scenic Puget Sound tour can be had by boarding a Washington State Ferry at Coleman dock for a cross-sound trip to Bainbridge Island (30 minutes one way), or Bremerton (50 minutes one way.) 

Pioneer Square: take the Underground Tour and make sure to visit the Klondike Gold Rush Museum, a National Historical Park run by the National Park Service (free), especially if you are going to Alaska. This itinerary will let you see much of Seattle in a short amount of time. 

Just a short walk East of Pioneer Square is Chinatown (International District) with its rich tapestry of supermarkets, small shops and Asian restaurants.

For tour companies try Customized Tours.  They have been around forever and are the only ones that do a winery and waterfall tour.  It's nice because it gets you outside the city.  Their city tour stops 4 times to let you get out, take pictures, and explore a little vs. just sitting on a bus.  Kids, families, and the young at heart tend to like the irreverent 90 minute Ride the Ducks Tour that leaves from the Space Needle or Westlake Center. If you're serious about sightseeing the other tour companies tend to offer a little more comprehensive view of Seattle.

Tours Northwest is perhaps the largest tour operator in Seattle and does many different tours including a pre and post Alaska cruise tour which helps visitors trying to fit in a tour before heading to the airport.  Their city tour is one of the only tours that will take you across Lake Washington on one of the floating bridges.

From Westlake Center you can also ride the Seattle Streetcar to the new South Lake Union Park.  On a sunny day the walk is very nice as you can watch the seaplanes take off to Victoria and the San Juan Islands.  The Museum of History and Industry (MOHAI) is also located here.  Adults and kids will enjoy the musuem and the telling of the entire history of Seattle.

Another weekend activity you can do at South Lake Union Park is to take a boat cruise from Argosy Cruises or Seattle Ferry Service.  Lake Union is the home of the Sleepless in Seattle houseboat and the cruise goes right by it. For those staying in the South Lake Union area both cruises are an easy walk from nearby hotels.  The AGC building on the west shore has a McCormicks and Schmicks which offers an incredible happy hour every day of the week.  Its a great location right on the water.   This is an enjoyable way to spend a few hours especially on a sunny day. 

Grab a copy of The Seattle Weekly or The Stranger to find out what is going on in Seattle. Both are free local papers published every Thursday and available locally at newstands, coffee shops and curb side paper boxes. They offer information on bars, music, movies and restaurants broken down by neighborhood. Please note that The Stranger it is an alternative paper and you might not want the kids to read it.

There is a  waterfront trolley 'bus' route 99 that will take you from Pioneer Square all the way to the end of the waterfront where you can visit the Seattle Art Musuem's Olympic Sculpture Garden just north of Pier 70. The route now goes along the waterfront thru Pioneer Square, Chinatown and up 1st ave past the Pike Place Mkt and to 1st and Cedar which is walking distance to the Space Needle.  It then goes down Broad Street past the sculpture garden and along the waterfront.   It runs approximately every 30 minutes during the day and early evening.

 http://metro.kingcounty.gov/cftemplat...

You can print out the online timetable for route 99.  It makes for an economical option versus paying for the hop on hop off bus.

Consider taking a day trip by bus from Seattle to the Musuem of FlightSnoqualmie Falls, or Mount Rainier.  These activities will take a half or whole day to complete.

Sightseeing by public transit video

This is a city sponsored video showing some highlights.  It was done before Lt Rail started running but the references to the Bus Tunnel and Westlake Station are the same ones used by the train from Seatac airport.

http://www.seattlechannel.org/videos/...

 http://metro.kingcounty.gov/cftemplat...

Off-Site Links:

Argosy Cruises

Seattle Ferry Service

Klondike Gold Rush Museum

Customized Tours of Seattle

Tours NorthWest