Yes, the ship building companies do host a tour, traditionally the first Saturday in May. Rotary International usually sponsors the event. The Calendar of Festivities will have more information closer to the date of the event.
No, regularly scheduled tours do not happen at any other time of the year. However, from the corner of First Avenue and Jefferson Street, during warm weather, Palmer Johnson (builder of luxury yachts) will have their gigantic garage doors open so that you may witness the huge hulls that they are constructing and working on. Turning 180 degrees from Palmer Johnson and looking northwest, you will see Bay Shipbuilding Company's southern edge. Follow First Avenue until it converges with Third Avenue and you will have the opportunity to see 1000 footers, barges, cargo ships, and tug-boats under construction through the fencing.
In addition, there is Great Lakes Yacht Services (GLYS)on the corner of Michigan Street and First Avenue just off of the Michigan Street Bridge. Check out the boats in winter storage from the walkway of the Michigan Street Bridge.
*Please respect the fences and perimeters of public areas. They are there for your safety.