Although you, as a W-2 employee, are not allowed to deduct out of town living expenses, on a temporary* assignment, your employer is allowed to deduct your expenses. So the best plan, tax wise, is for him to pay those expenses either directly or to reimburse you. It makes a difference if he reimburses you for actual expenses (an "accountable plan") or gives you an allowance. An allowance (without accountability) is usually taxable to you.
You didn't ask, but you will continue to be an IL resident while on the out of town assignment and pay IL state tax on your salary earned in TX**
*. In general, an out-of-town work assignment at a single location is considered to be temporary, which is a prerequisite for deducting travel expenses, if it is realistically expected to last one year or less and does in fact last that long. https://www.ehtc.com/resources/news-articles/bid/111175/Deductions-for-Temporary-Out-of-Town-Work-As...
At the point, in time, when you know the assignment will be permanent, the expenses are no longer deductible.
** The general rule is: your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state.
Since TX does not have an income tax, you do not have a non-resident return to file. But you still have to pay tax on that income to your home state.
