I teach part-time at several colleges. Many times in 2017 I traveled from one college directly to another college to teach a course (before coming home). In fact, I traveled to three colleges in a row (twice a week) for a semester last fall. Can these miles be deducted?
Yes, if you itemize deductions (Schedule A) you may deduct the cost of driving between job sites. As you noted, the trip from your home to the first college of the day and the trip from the last college of the day to your home are nondeductible commuting expenses. Your mileage won't be fully deductible as it is a part of the miscellaneous deductions that are subject to the 2% rule.
To enter your job-related mileage in TurboTax, please follow the instructions in this FAQ: Where do I enter job-related employee expenses? (Form 2106)