Do we need a business license?
We offer engineering, construction, and maintenance for the Telecom industry.
Without knowing the full nature of your business it is hard to answer your question specifically. If these are commercial projects, for example, contracted commercial construction, you would need to file your Virginia S-Corp as a foreign entity in those states and may be required to obtain certain city permits or business insurance policies once you have the foreign entity registration complete.
I would recommend you to consult with a business attorney, and research the specific regulations of each state and city where you would be conducting your business.