The great sights attract visitors, and regretably visitors mean crowds and tacky tourist attractions.
A good strategy for such places is to spend the night and see them before and after the main wave of tour buses. You could see a good bit of what Carcassone has to offer in this fashion staying one night, or if you stay longer there are interesting sights in the area that you can visit in the afternoon.
If you go I think it is worth getting a room in the old city (which is separate from the rest of the town) precisely to be able to enjoy the evening and morning there. There is also a guided tour which includes access to the castle and is worthwhile.