It has been rumoured that the upcoming third Doctor Who Adventure Game will allow players to explore the TARDIS, but whilst we wait to hear further news, there is another way to do just that right now.
Mod developer Demeggy has re-created the entire TARDIS to explore and use in the game Fallout 3. The mod is part of a quest called Fallout Who: The Last Child of Gallifrey. All you need to run it is a PC copy of Fallout 3. Then download the mod and follow the installation instructions from here and away you go.
You begin the quest in an abandoned UNIT base where you find the TARDIS. Once inside, you can go beyond the console room (Tennant era), take a swim and even try out the Doctor’s wardrobe. Later on you get to fly the TARDIS. It’s really impressive especially considering only one person worked on it.
Fun fact: In the original Fallout in 1997, the actual developers put the TARDIS in as an easter egg.