There doesn't appear to be any rule stating that a wizard cannot teleport inside of a living being, nor is there any rule stating that a wizard cannot teleport inside of a solid object, specifically, although "Areas of strong physical or magical energy may make teleportation more hazardous or even impossible." The inside of a solid object would quite likely constitute an area of strong physical energy. Whether this makes teleportation impossible, or merely hazardous, is subject to DM interpretation.
Teleporting inside of hollow spaces, on the other hand, appears to be entirely permissible. Thus, you can teleport inside of a hollow tree, a bladder, or an inner ear, provided you can actually physically fit in such a space. If you don't fit, see above for teleportation into solid objects: "impossible or merely hazardous".
However, interplanar travel is not permitted: That means a wizard in an airplane cannot teleport onto another airplane, although intraplanar travel is permitted, so a wizard sitting in first class could teleport himself into the bathroom. The wizard may or may not be able to teleport off of the plane entirely, at the DM's option, but will not be able to teleport back onto the plane should he leave, either by teleportation, or a door. Wizards attempting to use Fly to board the plane run the risk of being sucked into a jet engine.