You can regain access to Vault 101 by taking the Quest "Trouble on the Homefront", which can be taken by listening to an emergency Radio broadcast that is automatically picked up in the vicinity of Vault 101, after you have completed the main Quest "The Waters of Life". This quest involves bringing peace to a troubled Vault 101, that was thrown into turmoil following your escape. As such, you will be able to fully explore all of Vault 101 for the duration of the Quest, and speak to any of the inhabitants that didn't die during your escape from the Overseer.