For the more well known places that are already mentioned you have to overnight to make it worthwhile. But just around Paris is surprisingly enough lovely countryside to enjoy if you just want to visit it for a day.
South-west there is the Parc of the Chevreuse Valley. Follow the D91 from Versailles to Rambouillet. Nice is Dampierre-en-Yveline and certainly the abbey of Les Vaux de Cernay. Further Château de Breteuil is worth a detour. Rambouillet is a nice place to visit for it’s château and the park. If you like you can drive further to Château de Maintenon, the one I would place on top of the list as it is not too big but gorgeous. Adding Chartres will (likely?) be too much, but think it can be the place for dropping the car and taking the train back to Paris, so avoiding rush hour.
Also the Vexin region north of Giverny is really lovely, but you have to know the best places. I have followed a scenic route with my car there last month and can give you details if it interests you.
A bit further south of Compiègne (including Senlis and Chantilly) offers enough for a drive through the countryside. Explored the region last month too and the same as the Vexin region there is enough to enjoy. If of interest I can give you more details.
To avoid rush hour around Paris, best is taking the train for renting the car somewhere outside and bring it back to a place for taking the train “home”.