Depending if you want a boat or a space to live on in the water there are several options. I saw 2 liveaboard houses in Lake Union for between $150k and $170k but you can mortgage those through a bank, although slip fees for those were above $340 a month.
Otherwise you need to find a boat that comes with liveaboard status and you may need a brokers help for that. They do come up but are limited because Seattle isn't allowing any new liveaboards at least in fresh water.
Shileshole is remodelling until 2008 so they are not taking anyone from their waiting list until they replace their docks. It may be a good time to get on their waiting list if you don't find a boat that has liveaboard status.
Also check Salmon Bay Marina, they have some liveaboards and control their own brokerage. They have a website that I don't recall.
In Lake Washington check Parkshore Marina. It is condo, but you can rent from an owner and liveaboard for a fee. Then you just need to get a boat to put in there.