Is anyone aware of an open access database with companies/large employers registered in a given city in US, specifying registration date (office opening).
The OpenCorporates data is the closest dataset that I know of. It includes the registration information for many U.S. states, but not all.
There's a fair amount of corporate registration data on Enigma Public (disclaimer: I work there and legitimately vouch for it). It's organized on a state by state basis but you should be able to see the city where a business is registered within the dataset. Here's California, Texas and New York. We definitely have other states too - I would just search 'Corporate Registration' in Public's search engine and see what comes up.