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
I remember back in the bright college days, the school took us for a week in Rome, I was nineteen years old then and still consider it one the most elated moments of my young life.