You don't say if driving or flying so I'll start with flying in. If budget is a concern hotels out by the airport are more reasonable . Getting into town can be accomplished by rail.
hotels in Seattle run the gamut of course large to botique. Prices also. There are only two hotels close to where the solstice will dock if they use the downtown dock as normal.
The Edgewater and the marriott waterfront.
As there is a walker involved I'm not sure either of those is close enough. Google maps would allow you to figure that out.
other than that all other hotels would require a cab and your budget would be your only consideration as most are all about the same distance away. For one or two nights I would use Hotwire 3/4 star in Seattle works well.