Getting to Seattle
Your air travel: Seattle-Tacoma International Airport (SEA) is the airport. It's in a town called Seatac. I wonder where they got that name. Many airlines fly here. From the airport: There is not great public transportation (read: buses) into the city from the airport. I recommend a cab or a shuttle. The shuttles are pretty easy to find in the airport, so you don't have to book in advance. You'll save a little money by shuttling rather than cabbing if you're traveling alone, but if you're with even one other person, a cab is probably very comparable, and much faster.
There is also a Gray Line bus that goes to downtown hotels. Taxis are also readily available, and there's a $28 flat rate into downtown, if that's where you're staying. To the U-District it should cost around $40 (and most of the way should be on the interstate, FYI), but it will be metered.
Where to Stay
The reception is at the University Tower Hotel in the neighborhood called the University District. (There's a university there.) It's cute (on the inside), and if you get a room over the 7th floor, there will be a great view. If you want to book a room with them for convenience's sake, you can contact them by visiting their website. It's not the fanciest, or the least fancy. It's OK, but since they weren't offering a deal to our guests, we didn't book a block of rooms.
We did book a few rooms at the College Inn. It's quaint, and far from fancy. There's a dive bar downstairs, and it's a big college hangout (the university is not in session, though). The good news is it's only ~$80/night. If you want to get a room there, mention my name (that's Ruby Kane), and they'll hook you up with ones they're holding for me. There are only a couple with two beds (in the whole hotel), so if that's what you're looking for, act fast. It's walking distance (maybe 4 long blocks) from the University Tower.
Otherwise, there are a couple of other hotels you can stay at in the "U District." (U is for university.) The University Inn and the Watertown Hotel are closest. The Silver Cloud is a pretty long walk away, but a short taxi ride.
If you decide you want to stay downtown, there are many, many things to choose from, and I can't list them all here. One tip for visitors is that "Seattle Center" is not downtown, which it may seem to be from the name. It's a Center in Seattle (and where our illustrious Space Needle resides). You can feel free to ask me about specific locations, and I'll find out about them; I don't personally stay in hotels in Seattle.
The gay area of town is Capitol Hill, but there are few places to stay there. Another Silver Cloud and a couple of B&Bs. A cab from the U District to downtown will probably cost around $15 ($20 tops). I don't recommend public transportation at night in Seattle; it's slow to arrive, not terribly easy to navigate, and stops running early (read: buses -- can you believe it???).