As with many things, the answer to this question depends greatly on the type of tutor you have employed. Obviously, after school or school-sponsored tutoring should take place at the school, though they may ask you to participate by sending snacks or asking for volunteer time. If you have chosen to enroll your child in a tutoring center, such as Score!, Kumon, or Sylvan, they generally have storefront locations where they provide their services. Finding out whether or not there are locations near you may help you decide if these are good options for your student.
When hiring a private tutor, however, there is usually more flexibility. Novice tutors, such as the high school senior who lives next door, may double as tutor and childcare, so use your best judgment as to what you are comfortable with. A professional tutor should always meet your student either in your home or on neutral territory, such as a public library or well-traveled café. Be weary of tutors who provide individual tutoring in their own homes, unless you have a previous relationship with them.
If it is ever necessary for your tutor to provide transportation for your student in their own vehicle, make sure this is something you have discussed ahead of time. You may rely heavily on your personal relationship with your tutor, but at minimum, verify that they are insured, and be clear on where they are going and when they should be expected back.