The newest Radeon graphic drivers are not working correctly with SimCity. The "fix" that seems to work is to install an older driver to use with SimCity. The last driver reported to fix it was non-whql-win7-64bit-radeon-software-crimson-relive-17.6.2-june13. Older AMD drivers can be found here: http://support.amd.com/en-us/download/desktop/previous?os=Windows%207%20-%2064 You may want to go into Origin, right-click the SimCity icon and repair game after installing the new driver, just for good measure.
I know that installing an older driver is not an optimal solution.