How you are treated by the Toyota people will be very different based on whether you are selling to them or they are selling to you, as you might expect. Of the three cities you are visiting, Nagoya has the least to offer tourist-wise, I presume you are going there because Toyota HQ is not far away. In fact, if that is your mean reason to visit, stay nearby rather than in Nagoya if there is a decent hotel.
Other than providing general guidebook advice (like the first two responses above), we can be more helpful if you are specific about the trip details, letting us know how many days you will be in each city, how much free time you will have, and the specific interests of the individuals concerned.