Is there a category to put dry cleaning and suit purchases related to the business as a deduction?

In general, no, there is not a place for that.  

If you incur dry cleaning expenses while traveling away from your tax home doing business, then the dry cleaning expense is claimed as a travel expense.

But, if you are talking about purchasing suits to wear while conducting business and the expense of dry cleaning those suits routinely, that is not considered a business expense, but a personal one.  The suits can be used for other purposes unrelated to business.  

To be able to claim an expense for clothing related to your business, it must be a uniform, safety gear, or other type of specialty clothing that would not reasonably be able to be worn for personal or non-business purposes.  If you did have expenses for this type of specialty clothing and the cleaning of that clothing, then the expense could be entered as a Miscellaneous business expense where you can enter a description and expense.