Arc - GIS is best for this. Q - GIS may also possible with these types and it is available to download free of charge. You can range the solar radiation data and do the mapping.
If you use Python, then there is a Python package available names as "Pysolar". It is a collection of python libraries which can simulate irradiation on any point on the earth by the sun. Follow this link:
http://pysolar.org/
Also, there are many software available for mapping solar radiations of any specific location. Such as Spatial Analyst tool of ArcGIS as well as QGIS software. You can input your data in .CSV file format to map solar radiations according to your requirements. There are other software as well such as RETScreen, PVSyst etc. RETScreen is free of charge (but user registration is required).