My wife is an independent investigator. We are currently looking for a house, but right now are living in a hotel. She has work in a city and will be doing the majority of the work from a hotel that we will be staying in. On the days she is working are those days that we pay for a hotel deductible as a business expense?

No.as you can see, in order for her office to qualify as a "home office," it must be used exclusively or regularly for business purposes. Exclusive usage means that her office is used solely for business purposes, and never for personal reasons. The home office deduction lets you deduct things like mortgage interest, insurance, utilities, repairs, and depreciation for the portion of your home used for business but you do nothave these expenses for the hotel room that you use.