Since it seems unlikely that these data are available already from the novel virus, I'll refer to other coronavirus strains associated with outbreaks, the SARS-CoV coronavirus associated with an outbreak in 2003 and MERS-CoV.
In reference to the stability of the virus outside the body for SARS-CoV, the WHO consensus document said:
Data from the Chinese University in Hong Kong indicated that SARS-CoV has
been isolated from stool on paper, a Formica surface and a plastered wall after 36 hours, on a plastic surface and stainless steel after 72 hours, and after 96 hours on a glass slide.
Hospital environmental samples from a number of sites, including walls and the ventilation
system, tested PCR positive in Canada.
A later follow-up confirmed that SARS-CoV is viable possibly for days in the right conditions:
In the present study, we have demonstrated that SARS CoV can survive at least two weeks after drying at temperature and humidity conditions found in an air-conditioned environment. The virus is stable for 3 weeks at room temperature in a liquid environment1
1Chan, K. H., Peiris, J. S., Lam, S. Y., Poon, L. L. M., Yuen, K. Y., & Seto, W. H. (2011). The effects of temperature and relative humidity on the viability of the SARS coronavirus. Advances in virology, 2011.
This suggests that SARS-CoV was better at surviving in the environment than other related strains, especially in cool temperatures. However, there was still a substantial decrease in viral titre by 1 week.
MERS-CoV virus could still be recovered after 48 hours2
...on plastic and steel surfaces, though not at 72 hours, at 20C. The virus degraded more quickly at higher temperatures.
2Van Doremalen, N., Bushmaker, T., & Munster, V. J. (2013). Stability of Middle East respiratory syndrome coronavirus (MERS-CoV) under different environmental conditions. Eurosurveillance, 18(38), 20590.
Assuming the new 2019-nCoV virus is similar to these, there is a risk of environmental transmission particularly in high-exposure locations like hospitals. It seems far less likely to be a risk after multiple weeks, but there is still little known about the new strain.
I was unable to find more than speculation about rates of actual infection due to exposure in these conditions, but that speculation is mostly focused on the health care setting and in particular on transmission in health care settings despite extensive precautions.
It's very difficult to connect culture viability to actual transmission risks, and not really ethical to swipe different concentrations of a coronavirus on the surfaces of a room and let people wander through to see how many get sick. Therefore, the best evidence for surface transmission of these viruses is when other methods of exposure can be mostly ruled out, and this is a very imperfect estimate.