After entering the Keep and getting the quests from the board at the provisioner and the Undertaker I can't find a way to access any areas other than outside the keep and then the exit to the Cemetery. Am I missing something? I thought that obtaining the quests would open new areas up.
Bring up the World Map by hitting the "m" key while you are in the keep. That's how you travel to the other locations outside of the keep. You must be in the keep courtyard to do that, the same map where the marketplace is, you can't do it from an indoor map such as the tavern or the provisioner's, etc. You also can't do it from the area directly outside of the keep where the cemetery is, even though that's what your instincts might tell you.
A good rule of thumb is that if you have to exit the area via a door icon you can't access the world map from that area.