I let the client decide. If the parent is comfortable with me coming to their house, I will. My biggest concern is whether or not distractions at the home, such as siblings, electronic distractions, etc., will complicate the instruction. I prefer "neutral ground" like a public library, given a choice, where it is quiet and distraction-free.
A match between the tutor's conducting their business and the student's comfort zone would be the ideal. However, there ought be some sort of flexibility in order to reach a compromise. That is to say, a win-win negotiation where neither comes out to inconvenient. It is true that Wyzant tutors, as independent contractors earn their income as supplement, but the ultimate goal is, what will be the most beneficial for the student's learning experience ? My personal opinion is that the tutor ought to be the one to know how to adapt not only the student's learning style, but also be flexible towards the student's best learning environment as much as possible. Especially if the student is a child or teenager. The bottom line is, the tutor is to find out the best learning environment and learning style of the student and make it work together (including making the best use of Wyzant's tools such as the online tutoring, etc)