Neuilly-sur-Seine has the advantage of being very close to the city and the woods, Versailles is farther in the West, but has an idiosyncrasy of sorts. Saint-Germain-en-Laye might be an option. Other towns are charming (Garches, Marnes-la-Coquette, Ville d'Avray, etc.), but smaller and thus perhaps of a lesser interest for a short stay.
Are you planning to travel with your family?