How are you liking Seattle so far?
I like it a lot. When I moved here I had no idea where I am going (I did immigrate from outside US). Almost 15 years later, I've been to a lot of places in the USA and Seattle is still one of my favorites. The city and the nature around it are quite beautiful, there is plenty to do, finding jobs, at least in previous career, was piece of cake. The only reason I would move from here is that it has been quite a while since I've lived anywhere else and I am getting a bit restless.
Umm, the space needle I guess? I don't know much else about Seattle otherwise. If you were going to pick one or two other "must see" places to go, what would they be?
Well, the Space Needle is actually not a bad idea.
You'll most likely see it from the highway anyway but it is still worth visiting. The area around it is known as Seattle Center, it's a mix of a park and museums/other culture venues. During the summer and early fall they tend to have events on weekends, so you can expect a lot outdoor performances, etc. On the same block are EMP (Paul Allen's museum of music, ?? Music Project) and the Sci-Fi musem.
What I don't recommend is actually going up on the Space Needle. The restaurant is overpriced and not that good (second hand info). The view is ok, but if you want a view of Seattle from a high rise, you're better of heading downtown to Columbia Center. This is the tallest building in Seattle, owned by Bank of America. It is not advertised much as a tourist attraction but for $5 they'll let you go to the observation deck on top of the building. Cheaper, less crowded and taller than Spaced Needle - what's not to like.
While in downtown, you may want to visit the waterfront. It is what you would expect - a sidewalk along the ocean with pier, stores, restaurants, etc. It is somewhat loud (there is a highway nearby) but the views are good. If you keep following that North, you'll end up in the Olympic Sculpture Park - that's nice to see too. Also in downtown, Seattle Art Museum.
More things in the same area - Pike Place market, very popular between tourists. The first Starbucks ever is there as well. Within a few block are some night clubs with live music, if that's your type of thing. For more night live, head north on 1st or 2nd Ave in Bell town or East (15-30 min) to Capitol Hill. The former is where the "fancy" places are and the latter where the hipsters would be.
If you are driving, you may want to go to Alki beach - about 15 min away from downtown. It's on the other side of Elliot bay, across from downtown. Nice walks, great views of downtown and the mountains behind it, cafes, restaurants, etc.
There's probably more but I think this is a start. If you have any specific questions or want a longer list - let me know.
PS: I'm not sure if it will stay the same in the link, but today's picture of Yahoo weather in Seattle is taken from Alki:
http://weather.yahoo.com/united-states/washington/seattle-2490383/