Oh, yeah...it's pricey! I suggest you go someplace like Hotels.com to find one. You will want something in downtown Seattle, if you can find something affordable for you. If you're in the suburbs, you will deal with horrible traffic congestion to get downtown to explore. Or near Seattle Center so you can take the monorail into downtown.
I'm not real comfortable making specific recommendations because I haven't stayed in downtown Seattle for about ten years. Our trips there are generally day trips. The few times in recent years that we've spent the night, we've stayed with various relatives who live in the suburbs.
Anyway, ten years ago, the Travelodge by the Space Needle was decent. Not fancy, but clean. And I just checked the prices at Hotels.com and at the Travelodge website. While the chain's own websites are often cheaper, in this case the Travelodge website quoted $120 but $102 at Hotels.com.
Like I said, you can take the monorail to the downtown area and walk to the places I recommended in a previous post.
Check around and see what else you find. If you want, let me know what you're thinking of and what area it's in. I may not know the hotel but I could probably tell you the plusses/minuses of staying in certain parts of Seattle.
Note that if you're planning on doing the beaches in the Kalaloch area (First, Second, Third, and Ruby Beaches), lodging is really precious here. The only place to stay that is close by is at either the Kalaloch campgrounds or at the lodge. That's it. And they are VERY popular. Get your reservations here.
It's been a couple years since we've camped there but I'm assuming they still have the overflow area. Now, this is more like camping in a big gravel parking lot with some patches of grass around the perimeter. Not really a pleasant tent camping location. Especially because the lack of trees/brush means that the wind can really whip through there. But, if you can't get a spot in the campground, it's really your only other option in that area unless you spring for a room in the lodge or one of the cabins. And, when we were there, I think they only charged $3/night for the overflow.