I am not aware of any Chateau right by the Disney area that is super easy to get to via train since most train connections require you to go into Paris first. I've done entire Paris trips by train/walking & had a great time, but it sure is a lot easier if you stay near a main train hub (i.e. in Paris).
As for Chateau, Malmaison, Fontainebleau (lots of walking), Rambouillet, Chantilly are all in the Paris vicinity. Some other relatively close day trips from the area are Chartres (easy walk from train to Cathedral), & Epernay (reasonable walk from train station to Moet & some others). There is some type of bus service from Chessy to Provins (google provins to chessy bus - had looked at it when I was considering train/bus only).
When we went recently, we decided to rent a car. It gave a lot of flexibility & saved a lot of time compared to the train/bus, but you can do the train/bus only trip. The rate for renting a car turned out to be pretty reasonable, too (shopped around a lot, AutoEurope is supposed to be good but we found Hertz with discount codes for cheaper).