Fontainebleau

10 million people visit the Palace of Versailles every year and that is why I have never been. But if you have an extra day or two I highly recommend jumping the train to Fontainebleau (from Gare de Lyon) and renting a car. Yes, the car rental agency outside of the city may not have English speaking staff like in Paris, but it is totally worth all the pointing and shrugging to avoid the drive out and back through the City of Traffic Lights. Be clear that your car insurance is covered by your credit card (it is, right?) since that will be the most expensive question to get wrong. They may also put a deposit on the credit card for damages, not because you look shifty, but because, well, there is a lot to scrape against on windy, narrow European streets.

300,000 people visit the Royal Château of Fontainebleau and it is probably more than you can do in a day so spend the night locally. Stroll the small town and find a hearty country meal with an equally hearty country wine.