Subject: France
Hello Erina, The best spelunking is in the Dordogne. Alas, as just mentioned before, the caves of Lascaux are off limits, to protect the cave paintings. There's also good spelunking north of Nice, but too far for a 4-day trip from Paris. My immediate thought of an interesting town was Strasbourg, already mentioned by Linda. A historic city, on the crossroads of two cultures, with the green Vosges nearby, a fantastic hiking area in September, but perhaps not ideal for your family. Still, the mix of history, the wonderful green mountains, the superb cuisine and wine of the Alsace, make it my favorite region of France, after Provence.

Speaking of Provence, I second the idea of taking the TGV to Avignon (less than 3 hrs. from Paris, I believe). The town has much to offer, Palais des Papes, le pont and much more. Then I would suggest to rent a car for a day or two and visit Isle-le-Sorgue (fantastic antiques market on the weekend, esp. Sund.), St. RÈmy, Les Baux, and a stop at Maussane for the best olive oil in the world. Provence is very much alive in September and your mother will have the time of her life doing the markets in the villages and towns.