Self-sustaining underground city

One of the reason's cited by those advocating the colonisation of Mars or the Moon (or orbital, or Venus) is to provide a refuge for humanity in the event of any catastrophe on Earth. A couple of quotes from Elon Musk on the subject are reproduced below (from the Guardian):

"It's sort of a futuristic version of Gibbon's Decline and Fall of the Roman Empire. Let's say you were at the peak of the Roman empire, what would you do, what action could you take, to minimise decline?"

"The lessons of history would suggest that civilisations move in cycles. You can track that back quite far – the Babylonians, the Sumerians, followed by the Egyptians, the Romans, China. We're obviously in a very upward cycle right now and hopefully that remains the case. But it may not. There could be some series of events that cause that technology level to decline. Given that this is the first time in 4.5bn years where it's been possible for humanity to extend life beyond Earth, it seems like we'd be wise to act while the window was open and not count on the fact it will be open a long time."

Whilst I entirely agree with doing what we can preserve intelligent life and civilisation, and I am keen that we colonise the solar system, I wonder whether there is a more cost-effective way to create such a refuge here on Earth.

It should be possible with current technology to build a self-sustaining underground city on Earth (or potentially many). Powered by geothermal energy, the city could be a closed ecosystem that recycled all air and nutrients. Food would be grown hydroponically.

In addition to recycling resources it may be possible for such a city to undertake a self-sustaining mining operation (by self-sustaining I mean that enough resources of the right types are extracted to maintain and create additional mining equipment). This would allow the city to slowly increase the living area to support population growth, and to develop further geothermal power sources to increase resource availability.

The city would be connected to the rest of humanity via the Internet, but would otherwise not be connected except in the event of a disaster in the colony. It is important to maintain this separation such that a pandemic affecting the surface world would not affect the underground world.

Advantages over a Moon/Mars/orbital refuge:

• Proximity to Earth's surface for construction (particularly given the enormous cost of transporting material off the Earth's surface)
• Proximity to Earth's surface for recolonisation
• Proximity to Earth's surface for assistance in the event of disaster in the colony
• Earth gravity
• No additional latency in communicate with Earth's surface

Disadvantages compared with a Moon/Mars/orbital refuge:

• Could potentially suffer from some of the same catastrophes that affect the Earth's surface (e.g. if directly targetted by a nuclear weapon)
• Potentially lower availability of energy / resources
• Separation from the economy of Earth's surface would be artificial
• The proximity to Earth's surface would make such an endeavor feel less like a colony, with members (particularly second and later generation members) wanting to abandon the colony and rejoin the population on the Earth's surface