It's hard to come to this conclusion, but most of New Orleans should not be rebuilt. No one knows if it's even technically feasible; no one knows what the total cost might be if it is; no one knows how long it would take; no one knows how long America's attention will last and how soon commitment will wane. Promising to rebuild, holding out possibly false hope for tens of thousands of former residents, putting them in harm's way again in a geography doomed to repeated attacks by nature, none of this would be doing New Orleans justice.
Those parts of New Orleans on relatively high ground, where the original city was founded, should be given whatever assistance is needed to restore New Orleans to a viable, if smaller, city. But much of New Orleans, built below sea level as population growth expanded the city limits out from its historic footprint, should be given back to nature. Instead, government, business, and charities should focus on helping the displaced residents of New Orleans start life anew on higher ground, outside New Orleans, in neighboring cities and states or wherever residents choose. This itself will be a huge and expensive task. The purpose is not to avoid the cost of rebuilding. It's to focus the investment on an achievable end rather than waste it on a quixotic mission to restore what can never be restored.
Finally, the US should build a monument in New Orleans, dedicated to the dead and displaced, marking the first great city of the world to be lost to global warming. Increased ocean temperatures, more intense hurricanes, rising sea levels, and lost marshes and coastal buffers all forecast that New Orleans won't be the last city to be threatened with this fate. Perhaps New Orleans' legacy will be to inspire us to take action now to prevent this calamity from ever being repeated.