I’m looking at spending about a week in Seattle over the summer and was hoping to find some reasonably cheap lodging. I’ve done a little research and found some hotels around $50 a night as well as some hostels for $20 a night ($50 for a private room). I’ve never stayed in a hostel before and the idea of dorm-style accomodations doesn’t really suit my style but it’s a lot closer to my budget. What’s the best bang for my buck?
Refridgerator box under the Alaska Way viaduct–excellent company, near shopping, clubs, fine dining & easy highway access; waterfront view. $0/night, but you might want to bribe your neighbors with a $5 bottle of MD 20/20 to leave you alone. 
I don’t have an affirmative recommendation, as I’ve never had to look for anything like this, but I can give you a warning of what to avoid: If any of the hotels/motels you’re looking at have an address on Aurora Avenue (or Highway 99) with a block number between 4000 and 12000, cross them off. There are some reputable establishments there, but there are also a whole lot of fleabag outfits that cater to the prostitution trade.
I do know there are some pretty good hostels in the city, mostly downtown or (IIRC) near the university. If you can give us a specific name of a candidate facility you’ve found, we can respond with anything we know about it.