Daytrip castles outside Paris

There are some good opportunities, for example:

Fontainebleau (outer suburbs to the south-east, about 45 minutes by train from Gare de Lyon + 30 minutes of bus from Gare de Fontainebleau-Avon to the palace)

Vincennes (inner suburbs to the east, terminal of metro line ??)

Chantilly (northern suburbs, about 1 hour: take a train from gare du Nord (or the slower RER line D) to Chantilly-Gouvieux, then a bus or a fixed-rate taxi for the remaining 2km)

Breteuil (outer in the countryside to the south-west, requires a car, or ~40min by RER B to Saint-Rémy-les-Chevreuse then a 6km bicycle ride)

Vaux-le-Vicomte (south-eastern suburbs; 30 minute train ride to Melun, then bicycle or taxi, or buses some days)

Pierrefonds (north near Compiègne, about 1½ hour by train + bus)

Thoiry, best known for its drive-through zoological garden (out in the countryside to the west, only accessible by car, or by bus tours some days)

Saint Jean de Beauregard (southern suburbs near Les Ulis, about 1 hour by train + bus + a short walk)

Monte-Cristo (western suburbs near Saint-Germain-en-Laye, about 1 hour by train + bus)

Roflcopter already covered a lot, I can add: Giverny which has Claude Monet's house and gardens. If you are interested in impressionism, this is a mustdo

Other destinations doable in one day if you have a car are: Vezelay and Honfleur

I would really recomend Rambouillet.

From Wikipedia:

Rambouillet [...] is famous for its historical castle, the Château de Rambouillet, which hosted several international summits. Due to its proximity to Paris and Versailles, Rambouillet has long been an occasional seat of government.

[...]

Rambouillet is served by the SNCF Rambouillet train station on the Transilien Paris – Montparnasse suburban rail line to Chartres.

It's really easy to get to there from Gare Montparnasse using Mobilis ticket (14 euro/day normal fare or 7 europ/day if youre less than 25 y.o.).