There are several great palaces and châteaux located just a short drive from Paris. Palace of Versailles, Château de Pierrefonds, Château de Fontainebleau, Château de Chantilly, Château de Maisons-Laffitte and others are open for visitors.
If you don't feel like using public transportation or renting a car, take a tour: there are buses that leave from central Paris. The most interesting tours are:
The Palace of Versailles and the Trianon, a full day guided tour
A trip to the Château de Chantilly
Mont Saint Michel, a guided tour
You are in France, and it might be a good idea to visit the famous Champagne with a tour.
If you are not taking a tour and visit the châteaux and museums on your own, please make sure you double-check the hours as schedule is subject to change, especially during the winter months.