Following is svartkatt's Essential One-Day Seattle Must-See Itinerary. I wrote some of this up a while ago for a friend, and have added a little more. Hope it's useful!
Pike Place Market, definitely, and the whole area around there. Pike Place Market is actually a rather large area that includes the main building at First and Pike, Post Alley and Pike Place. The main building is several floors deep, and the section across Pike Place has an interesting maze of shops and little restaurants, and the original Starbucks is there. At the north end of the Market is Victor Steinbrueck Park, which is sort of the end of the Market area.
First Ave from Virginia Street south to Pioneer Square is a great walk. If you start at the Market and walk south, be sure to stop at Harbor Steps on First (across from the Seattle Art Museum) - it's a nice outdoor plaza that leads down to the Waterfront. One block north of the Seattle Art Museum and across the street from Harbor Steps on First Ave, check out Vetri Glass Gallery
Vetri International Glass (free) and the (also free) William Traver Gallery in the same building (upstairs, entrance around the corner on Union) for a taste of Seattle's glass art scene - one of the biggest glass art communities in the world. Bill Traver's gallery especially has rotating exhibits by many renowned local and international artists.
Continue down First to Pioneer Square (First and Yesler), the historic center of Seattle, best enjoyed in the mornings or early afternoon (it gets a little seedy later in the day, and the bars fill with drunken college kids at night). There are many galleries and shops along the way, and beautifully preserved historic buildings. After Pioneer Square, continue south on First to Jackson, take a left, go one block, and left again onto Occidental, a charming pedestian street with galleries and a great coffee house, Caffe Umbria.
*Definitely* visit the Central Library
The Seattle Public Library: Central Library - Plan a Visit (4th between Spring and Madison). It's a stunning building. Duck into the lobby of Benaroya Hall (3rd and University) to check out the immense glass chandeliers by Dale Chihuly, our celebrity glass artist. If you're staying in a downtown hotel, you'll probably be able to walk the rest of downtown: Westlake Square, 5th Avenue and the Pike/Pine corridor are sort of the main streets.
Sculpture Park
Olympic Sculpture Park: Visitor Information in Belltown (immediately north of downtown) is free and has great views. From there, walk down to the waterfront, and stroll back into downtown. Stop at Bell Harbor Conference Center
Seattle Convention Center, Seattle Washington Convention Center Bell Harbor on the way and head up to the open rooftop deck (free) for a nice view of downtown, the Sound, and the waterfront. Then continue back along the waterfront until you reach the Pike Hill Climb, which will take you back up to First Ave and the Market.
If you want sort of an all-in-one tour and $31 to spare, you can take an Argosy cruise from downtown. It goes north through the Sound with great views of downtown, around Magnolia Bluff, through the ship canal and the locks, and down past the houseboats to Lake Union, with nice views of Seattle as you end the tour (then they bus you back downtown). It's a little chatty for my taste as it's a guided tour, but you see a lot in a short amount of time that you wouldn't see otherwise.
Seattle Locks Cruise and Sightseeing Tour : Argosy Cruises In Seattle (make sure you take the locks tour - the Harbor tour just circles Elliott Bay). The ferry to Bainbridge is a cheaper option to experience Seattle from the water (30 minutes each way). You can walk around the town of Winslow if you like (it's a 15 to 20-minute walk from the ferry terminal, but if you're pressed for time, just come right back - for a one day trip I wouldn't say it's a must-see place). The views from the ferry are amazing though, especially as you come into downtown. It's also enjoyable in the evening when the city is all lit up. It's been getting dark here around 5 PM, so if you went over around 3:30 or 4:00, you would get daylight and evening views.
For views, if you have time during a work day, check out the 73rd floor observation room at Columbia Tower (M-F, closes at 4:30) for amazing views of Seattle and Puget Sound.
Columbia Center Observation Deck - Pioneer Square - Seattle, WA. It's $5 instead of $16 at the Space Needle. But the Space Needle is an icon, and worth it if you're a first-time visitor - you can take the monorail there from Westlake mall at 5th and Pine. Kerry Park on Queen Anne Hill, north of downtown, has hands-down the best view of Seattle, and is one of the views you see on postcards. You can drive or cab it up there - they'll wait while you jump out and snap some photos.
http://www.seattle.gov/parks/park_detail.asp?ID=342.
Not essential, especially for one day, but if you have the time:
Uwajimaya Asian market
Uwajimaya is a popular destination. It's in the International District (ID or Chinatown) just southeast of Pioneer Square, the historic district. The rest of the ID is kind of run down, but there are always lots of tourists at Uwajimaya. Be sure to check out the geoducks in the seafood section! If you have a car and depending on time, the Museum of Flight
Home | The Museum of Flight is pretty amazing, even if you're not that into airplanes. Experience Music Project and Sci-Fi Museum right next to the Space Needle is okay, but expensive, crowded, and not one of my must-see items. In fact I only went there for the first time this year. It was good, but I wasn't blown away, especially for the price. The University of Washington campus is beautiful - again these are further afield and not essential in a short trip.
Restaurants - what do you like? We have a pretty amazing restaurant scene here - fusion cuisine, seafood and Asian food are big here. There are some excellent Thai and Vietnamese restaurants, and fresh seafood abounds. The popular restaurants are packed here in the evenings, so I would make a reservation if you can, unless you mind sitting at the bar. My personal haunts include Matt's in the Market, Union, Zoe, Lola, Dahlia Lounge, Bambuza, Maximilian, Flying Fish, Shiro for sushi (atmosphere is so-so, but sit at the bar - if you like sushi/sashimi, this guy is amazing). There are also tons of smaller informal cafes and restaurants, especially around the Market. Starbucks is everywhere, but we have many fine local coffeehouses that will make you a much better cup of coffee: Caffe Ladro, Caffe Umbria, Cherry Street Coffee, Stella, etc. There are tons of them all over the place.
Do you have a rain-proof coat with a hood? It's been raining cats and dogs here, and if it's windy downtown, your umbrella will almost certainly be blown to smithereens. Hopefully you'll get a break in the weather when you're here! Hope you enjoy your visit.