Tenpenny Tower remained intact after the Great War and was discovered by Allistair Tenpenny, who rebuilt the place and now allows people from all around to take refuge inside its walls.
Fun Fact: Herbert "Daring" Dashwood can be found in the tower and can be talked to.
In The Main Quest
If you choose to accumulate evil Karma and destroy the town of Megaton during the game, you must report to Tenpenny Tower in order to switch the detonation trigger for the bomb with Mr. Burke and Alistair Tenpenny himself. Completing 'The Power of Atom' this way will allow you to take up free residence in Tenpenny Tower, giving you a place to get Purified Water for free and to store your bobble-head collectables.
The "Tenpenny Tower" side quest involves you trying to get ghouls moved into the tower, to the dismay of the residents there. There are different ways to solve this quest. One way is to simply kill all of the ghouls as you were told to, thus completing the quest rather quickly. Another way is to convince the residents that the ghouls are harmless. If successful, the ghouls and humans will live together but after a few days the ghouls will kill all of the humans. The third way is to help the ghouls break into the tower, thus causing mass panic as the ghouls systematically eliminate everyone inside.