We may be making this up but English Harbour seems like it is probably the biggest tourist draw in Antigua outside of St. John's. Probably including St. John's too but unless you arrived by yacht you've likely already been to St. John's. This view is of English Harbour (near) and Falmouth harbour (further away).
There is a sprawling national park here centered around Nelson's Dockyard which is the flat semicircle of land across the harbor in this picture. This picture is taken from the visitor's center which is up on a bluff at the site of an old fort. Shirley's Heights which is another nearby bluff (with impressive views to Guadeloupe) is also part of the park as are a few other ruins.
As you can tell from the previous pictures, English Harbour is an impressive S-shaped inlet which is well protected from the weather and was well protected from enemies (three forts guarded the harbor).
Fort Berkeley is down near water level at the harbor entrance. You can walk out there from the dockyard. If you've been up at the visitor center or Shirley's Heights it doesn't add a whole lot to the view.
Nelson's dockyard here is the only Georgian dockyard in the world. Are you impressed? Antigua wants you to be impressed because they mention this about a hundred times throughout the park and during the history-of-Antigua multimedia presentation up at the interpretive center. What does it all mean? Basically, Georgian-Caribbean architecture.
I'm not sure what we expected at the dockyard but there are a variety of restaurants and shops just scattered through it. It's a little different from a simple restored historic site. The museum though is quite impressive (if small). It has an array of maritime relics and all the Lord Nelson you could want upstairs.
It's worth visiting the museum just to go upstairs and walk around on the outdoor terrace for the views. It's possible the dockyard becomes crowded at certain times of the year or day. While we visited it was largely deserted.
There were definitely more fish than people. Along the waterfront we saw numerous tarpon. There's also some fish of the smaller, more colorful coral reef variety. Our four-year old found this by far the most interesting part of the dockyards.
There are a couple ways to get here from St. John's, Jolly Harbour or elsewhere on the island. One route is Fig Tree Drive which parallels the southwest coast of the island. We heard a lot of strange things about Fig Tree Drive and our general reaction after the fact is... "What??" We found it to be plenty well maintained by Caribbean standards. Only a small part of the road dives inland through the rainforest and a short but steep climb over the mountains. The beaches on the southwest corner of the island with Montserrat in the distance were much more of a highlight for us.
Another route is to come across the center of the island in which case you'll pass near Betty's Hope - the picturesque sugar plantation ruins in this photo. The mill on the right is restored, the one on the left is what the vast majority of mills on Antigua look like and they are everywhere. Incidentally, finding Betty's Hope from the south is challenging (it's an unmarked dirt road). From the north side of the plantation there are signs.