If an employer pays for your hotel/apartment and travel/ expenses but then adds it back to your W2 as part of your income can you use as a deduction?

Yes, if it is included in your taxable wages you can enter the expenses as an employee business expense.  It sounds like your employer is not using an "accountable plan" for expense reimbursement, which is way it is included in your taxable income.

• Job related expenses or employee business expenses (for W2 income) are subject to 2% adjusted gross income, and then included as miscellaneous expenses on itemized deductions on Schedule A.  If you use the standard deduction it's because you didn't have enough overall  itemized deductions to benefit you. 
• Use the instructions below to enter your travel expenses for your employment that were included in your taxable income on your W2.

https://ttlc.intuit.com/replies/4800418

If my employer does not reimburse me for my everyday stays out of town for work in the office, can I deduct those weekly payments to hotels?

Would love to hear from you a  yes or no?  I am not a 1099.  

No. Starting in 2018, W-2 employees can no longer deduct job expenses, including out of town travel. 

Despite the June, 2019 date on the original post.  The original answer applies to the pre 2018 rules.

June 2019 was the date the old post transferred to the new forum.