If you're young, no family, and you're living in a loft, then this is the perfect time in your life to relocate. You could probably move everything absolutely critical to you (photo albums, books, clothing, etc.) in a few large boxes. Either expense a u-haul and move it yourself, or ship it fed-ex, and arrange for the company to pay for a furnished place in detroit. Or, if you'd prefer, shell out for new living stuff (dinnerware, furniture, etc.).
Definitely pocket the client's allocated travel budget (ask for more than 60%.. 75 or even 80 isn't out of the question, considering how many extra hours of productivity they'd get out of you.)
You're never too early for a nest-egg; cash like that will come in handy when you want to put a down payment on a house, or go on that around the world cruise for your honeymoon..