This museum has a great collection of prehistoric, Roman, and medieval artifacts from Bordeaux and the surrounding area. It's free, but if you don't read French (the info cards aren't translated) the foreign language audio guides for E2.20 are well worth it.
Things to do
This cathedral has a lovely exterior and an equally interesting interior. There are lots of smaller chapels in the aisles, so it's nice to poke around at your own leisure. The tower next door offers great views of the city but costs 5 euro to climb.
This much-remodeled church might be a little more plain on the inside, but the history here is fantastic. The namesake saint's coffin lies under the altar, and a 7th century sarcophagus hides in one of the chapels in the aisle. If you can find the sacristan, have him open the 11th century crypt for you. There's also a 4th century Christian burial site underneath the church, but it's only open in high summer.
Only a small part is left of this 3rd century Roman amphitheatre, but it should still be on your list of must-sees. Guided tours are only offered in high summer, but even in the off season it's nice to stand by the walls and try to imagine how Roman Bordeaux, or Burdigala as it was known, might have been.
This lovely garden is a great place to spend a few hours. Whether you go to read a book in the shade, have a picnic lunch, or just sunbathe, it's nice to find a thick patch of grass among all the shining white buildings of the city.