In a port city like Boston in the 1770's, how often would a new ship arrive in port? Was it as common as several each day or week? When a new ship did arrive, was there a "registration" process and how did it get "assigned" a spot where it could unload? How long did it usually take to unload and re-load a ship full of cargo?
First, some excellent work on this has been done by Ian Steele for an earlier period. See his The English Atlantic, 1675-1740. As an example, between 1696-1700, over 600 ships left England en route to the colonies, which is about 150 ships per year at a time when far fewer people lived in the colonies (from 250,000 to over 2 million).
Let's look at the ports of Maryland. Annapolis and Baltimore were large port cities, as far as North America in the 1770s are concerned. Certainly both combined are not the size of Boston, but they will give us a good metric. There were registrations of ships coming in and out of the ports, though not many have survived. They registered the ships, their captain, point of origin, vessel name, size of vessel, country where vessel was made and the material being imported. In terms of where it could unload, the ships often did not come to "port" in the same way as a modern ship. Most large carriers (more than say, 50 tons) would have held anchor in the harbor, while smaller row boats or schooners would transport the material and people to the docks. This was especially true of vessels containing convicts, indentured servants, or slaves, as the ships had a consistent problem with escapees (Examples include MD Gazette, 09/13/1759 and 8/11/1763.
Luckily, the Maryland Gazette is completely digitized and available online at the Maryland Archives. Throughout the summer months, there is a constant stream of ships coming and going. A rough estimate for the 1770s in Baltimore and Annapolis would see about 7-10 international vessels, and perhaps as many as 50 smaller coastal vessels. The coastal vessels would be carrying goods and people from the upcountry downriver to the ports, or even along the coast to ports in Virginia.
In terms of how long did it take to unload a ship of cargo, it would depend on the merchandise and how it was sold. It could take as little as a day to be unloaded and brought ashore, but some cargoes would be kept aboard the vessel for weeks at a time. It depended on if the cargo was living or not, who the owners were, and how it was being distributed. Most of the historical writing on this has been done on the slave trade, which is understandable.