Asteroids have very limited resources. That is not a good place to set up a colony. They are great resources for individual materials, but how much water and carbon will you have access to on an iron nickel asteroid?. How much metal ore will you have available on a carbonaceous one? Having a colony with easy access to them such as on Mars is one potential justification for a colony on Mars. The lack of gravity is also a very serious issue. We don't even know if Mars (best shot) or the Moon (longer shot) have sufficient gravity to allow humans to live there long term. At 38% of Earth's gravity it would seem likely humans can adapt to long term life on Mars. At 16% it seems possible on the Moon, but questionable. Asteroids on the other hand are much closer to 0g where we know there are major issues. Another key issue is critical mass. How many people can any asteroid support and is that enough to support a self sustaining colony?

The best place to set up a second branch of civilization is to find a location that most closely matches where we know we can live. That place is Mars based on current knowledge both for it's current resemblence to Earth and its long term potential to be made to match even closer. We'll see what Dawn shows us about Ceres and Vesta, they might be better options than the Moon or even Mars, but I doubt it. I will grant you that the potential for a comercial facility where people go to work for brief stints then return to Earth and have most of their supplies sent from Earth might be higher for asteroids than Mars due to potential concentration of resources and low escape velocity, but not a self sustaining colony.

Regards,
Mark