I've been in this situation before. I spent most of last year working in a different city (about 4 hours away), with a position that did not include housing. I ended up finding a relatively cheap apartment to sublet, since I have an apartment in DC with my boyfriend and didn't want to move, and the salary for the job made up the difference. I probably wouldn't have taken the job if it would have cost me money. But, it was a good job and really good experience, so for me it was worth it. I decided not to do it again this year, but it's not impossible to do it.
A number of companies that will have their own housing- either the theatre has apartments, or board members will "host" a visiting artist at their house for a few weeks. It might be worth saying to a potential employer "I'm really interested in this job, but don't have local housing- do you know of any good options?"