Maine

Don't think "centrally located" will do it. Think I;d look at working your way up the coast instead. Driving out on the peninsulas can take a fair amount of time, just to find 1 lighthouse. Depending when you go, driving along rt1 is pretty slow. Maybe a few nights in the Old Orchard Beach area, a few more around Boothbay, maybe near Rockport, then up to Mt Desert Is. If you're up for the drive and have passports you can hit Quoddy Head and Campobello for a few days too.

There maybe 65 or 70 light houses in Maine and they aren't all on a main road. 250 miles of coast as the crow flies but 3500 miles if you run a boat along it. Plan on spending a long time if you want to see very much of it, or plan on going back.

What exactly do you mean by "Early 2017"? Many campgrounds in New England don't open until maybe late May or early June or so.

If it's early enough, biking will be very adventuresome (and cold), hiking pretty adventuresome (and cold), and fishing mostly consist of huddling down and watching for a little flag to flip up (and, yes, also cold).

Bar Harbor area is probably about as reasonable a central-ish area as any. Acadia is a beautiful park. The Maine coast is fairly long, though, so moving about might be more practical than trying to have one single home base.

Here's a site that will give you all the lighthouses in the state:

http://www.newenglandlighthouses.net/maine.htmll

You might want to select a number of spots to stay in-each part of Maine is unique. Acadia is one of my favorite spots but the entire coast is beautiful.

Bar Harbor gives you access to Acadia National Park and the coast. One of the most beautiful areas of the country. Lot's of campgrounds, hiking in the NP and I'm guessing plenty of lighthouses to search out.