there are about 2 days worth of stuff in seattle that can be done on foot out of down town (hop the foot ferry from Vashon). If your into museums, there are a ton of great ones you can get to via bus. Museum of flight is one of the best in the country, so if you like planes and the history around them, that would be a great place to go. (half a day)
The space needle / science center is a great bet, just don't do the dinner thing. Its over rated, and over priced. Eat somewhere near by, or downtown instead. Google can find you some good places.
For a good one day in Seattle, I would hop the ferry across, walk down the waterfront and up to pike place, then over to west lake center, hop the monorail to Seattle Center, do that stuff, back to downtown and head south for a Sounders game. The Mariners are fucking gay, and I wish the Sonics took them when they left. Find a place to eat between seattle center and the game.
REI is also worth checking out if your into outdoors stuff, I take it for granted, but when I take visitors there they are blown away. walking distance from convention center bus station.
As for skate spots, I don't know of any good city spots, but finding a local park is probably your best bet. Pretty sure there is one at seattle center.
For hiking you have both the cascades and the olympics right there. Both Olympic NP and Rainier NP are HUGE. You will not see all of either park, so don't try. I would suggest a few 3-4 day trips, depending on how fast you can move. We have mountains here, and you will cover a lot of vertical, so keep that in mind. Also before you decide on a trail, keep in mind that quite a few are still washed out or have trees over them. Ask the local rangers when you sign in at the ranger station. To avoid the crowds I would suggest trails outside of Mt Rainier NP, and in the southern Olympics.