Say that instead of the game ending after Hoover Dam, you were allowed to continue playing - what would be some interesting missions to play post-ending?

I had a few ideas for missions after an NCR win.

1. Reprogramming Securitrons

The NCR has taken control of House's securitrons and is trying to reprogram them so they can be used by the NCR. In the mission you have to help them find a way of reprogramming them - options could include going to the Brotherhood for help and secretly giving control over to them or keeping them loyal to you with Yes Man and giving the appearance they're supporting the NCR.

2. Strip Troubles

With House gone, the NCR now has control of the Strip and troops are now allowed to carry weapons. This has caused some tensions with drunk and penniless NCR troops firing off their weapons. For the mission you have to help resolve a dispute between the Tops and the NCR following a gunfight in their casino.

3. Taxing the Casinos

Another result of NCR control of the Strip is that the casinos are now being taxed which, of course, they are not keen about. You have to resolve the dispute and can either side with the NCR or work with the Casino bosses and bribe NCR officals to reduce taxation levels.

4. Caesar's Remnants

Caesar had a vast network of spies, with the defeat of the Legion they have gone into hiding. You are tasked to help track down and find some higher up members of the Legion so they can be brought to justice. You have to travel across the Mojave to find these people, visiting the Fort which has been burnt to the ground by the Legion so no records or information can be taken by the NCR.

I think the post-ending missions would have to show that despite your chosen side winning, everything is not perfect. That you see examples of NCR corruption after the win, that the Legion has brought harm to groups it promised it would protect, that Yes Man and House have created insecurity outside New Vegas.