Sounds like you need lodging 2 nights per week. That works out to a little more than 8 nights per month on average. If (a big “if”) you found a room at a local hotel or motel for $75 per night average, then you are paying over $600 per month. More realistically, I’d expect to pay $800 or more per month on average for this option.
A better bet would be to look on
craigslist for apartments or rooms to rent in the area. I took a peek at the recent listings when pulling up that URL, and saw roommate ads in the $400 to $600 range, and a few cheap apartments between $600 and $700. Of course, you'd need to figure out associated costs for utilities and the like to determine whether this option makes sense.