The old city of Carcassonne is ancient and very imposing. It was originally constructed as a fortress to defend the French and Spanish border. To this end, the people of the city constructed massive fortifications, including double walls, a drawbridge, and a dry moat. The buildings in the old city are packed close together, forming a ring around the keep in the center, where the people of the city would cower in times of war.
Unfortunately, the city planners made a grave mistake. They got so carried away with building fortifications and defensive structures that they only dug two wells. When the city was laid siege, all the invading force had to do was poison the water, and the city council turned over the keys in a matter of days. These days, much of the old city is very well perserved. There aren't enemy forces laying siege or knights galavanting around on horseback, but the fortifications are still in place and the keep is open for tours.
Interestingly enough, the city's two doomed wells still survive today, although they are covered in Plexiglass and filled with an unsettling number of cigarrette butts. The highlight of the city is the square in the center. Here you will find several small restaurants packed tightly together, some offering live French music from local bands on Friday and Saturaday nights (not for the faint of heart).
Music aside, the food is quite excellent. Most of the restaurants are thoroughly French, and all of them have at least one of the duck dishes that characterize the region. After dinner, take a stroll around the ramparts. They form a veritable maze encircling the city, and at night they provide beautiful views of the valley below.
Unfortunately, there's not much to do in Carcassonne besides poking around and eating. It's rather like a museum where people have moved in and set up souvenir shops. It's beautiful to look at, but the continuing effort at preservation makes it almost impossible for the city to make any progress (no alternation of the old city is allowed). It's nice, for a bit, for after a while you'll probably want to move on to something more modern and more progressive.
Quick Tips:
The old city is nice to walk around, though there is very little else to do. Everything is close together and the streets are very narrow, so watch out for cars and insane mopeds that cruise around at all hours of the day and night. Visit one of the restaurants in the main square, and tour the keep if you're interested in history. Leave some time for wandering around the ramparts, and if you're there at night, have a ride on the lit carousel outside the main gate. Try to stay in the old city, but be prepared to pay a premium for the experience. If the hotels are booked or you don't want to shell out the extra money, find a nice hotel outside the old city (there are quite a few near the train station).
Best Way To Get Around:
Walk. The city is small, and you should have no problem seeing everything in a few hours. If you want to get from the new city to the old city, you will have to walk a long way uphill, or hire a cab, which will cost about 30€. If you choose to stay in one of the hotels close to the train station, there is a cabstand close by. Cars are not allowed in the old city, so if you plan to taking a cab back, call ahead or have the waiter call one if you eat at a restaurant.