what would be a nice place for one night with a two-year-old, in or near beaune?
Will you have a car? If so, check out logis-de-france.com. Small family-owned inns all over France usually with on-site parking.
A great chateau in the contryside is: http://chateauderosieres.com/mapuk.html
Just an hour outside Beaune. They love kids.
I stayed at the Hoten Henry II in Beaune, about 1/2 block outisde the city gate. Nice room convenient, and has parking with the hotel if needed. Check out the website.