This facility "Wuhan Jianghan Disease Prevention and Control Center" is actually very close to the market.
There's no street view there - seems probable this is just a normal office (there are restaurants in the same building)
https://www.google.com/maps/search/Wuhan+Jianghan+Disease+Pr...
It is about 14 km by car between the Market and the Institute of Virology.
What do you think about the Daily Mail article which says that the Wuhan Center for Disease Control and Prevention (WHCDC, not the Institute of Virology, my mistake) is 278 meters away? They state that virus research is being done there. From what I see on the map there are some Union Hospital buildings, but nothing specifically identified as the WHCDC.
Edit: part of the problem seems to be in searching for the exact names of the facilities.
I think Baidu Maps places WHCDC in the same complex identified in that Daily Mail article, directly across the street from the Huanan Seafood Market. (I'm a bit uncertain because I don't read Chinese, so please let me know if I've made a mistake here.)