Sorry, I don't know of any hostels.
Hotels I can help you with. I stayed at this Days Inn, so I know they're decent. Across the street is another place that's cheaper if you pay weekly.
Charleston, West Virginia - Days Inn Charleston East - Hotel, Motel, Lodging
The housing market is excellent so if you're looking for an apartment, you could make quick work of it through the charleston gazette the way I did with much thanks to other bloggers here.
If you're not planning on staying long, they do have other kinds of temporary apartments meant for monthly type corporate stays, but they're furnished and more expensive. I think they were running about $600.
Other regular rentals unfurnished were from $275 all the way up to $750. Hope that helps.
