That said, it's probably my least-favorite island that we've been to in the Caribbean, and when we took a cruise the next year that stopped at a few of the places on the OP's cruise, we opted to stay and relax on the ship in Antigua (which is really not like us at all, but I'd do it again). So, I'd suggest either staying on ship or just planning a beach day -- not really worth an expensive cruise excursion tour.
Just a little extra about Antigua.
Funny how people see things differently - it is probably one of my wife's favorite islands - we stayed 2 weeks. Since I already commented earlier about the *diving in Antigua, I'll go with things I found out that I could apply if I ever go back on a cruise ship (which is not likely to happen.)
*Regarding diving, although the diving is okay, the only reason I wouldn't dive here if on a cruise ship is because of taking a taxi (distance and time.)
I have a hard time justifying eating a meal off of a cruise ship, when I've already paid to eat on the ship, but around the Jolly Harbor Marina, about ½ hour taxi ride, are several excellent restaurants. We frequented them often over 2 weeks - spent ~$990 on restaurant meals (and about $200 on groceries.) Didn't really care too much about food cost as we only paid $75 for our 2 bedroom resort for the 2 weeks - our friends paid the other $75.
Jolly Beach, a 5 to 10 minute walk to the Jolly Harbor Marina, is/was a cruise ship beach excursion. There is a "cruise ship only" beach, which also had a restaurant/bar. If one wanted a nice, cheap beach day, they could easily take a taxi (~$20 for 2) to Jolly Beach, open to anyone, still make use of the restaurant/bar, or go to one of the restaurants around the marina. There are a lot of other nice beaches though from 15-45 minutes away and a taxi on your own will probably be cheaper than a cruise ship beach excursion.
As
@Rob9876 stated roads aren't great. We paid $79, including tip, for 2 to have a taxi (someone who knew the roads) take us on a 4 hour tour of the island - there are not that many sightseeing highlights - maybe cheaper than a cruise excursion though.
If the timing works, I would recommend a boat ride to Montserrat - half of the island is green and the other pretty barren due to the volcano (you can see it from Antigua. If it were a cruise ship excursion, it is something definitely worth doing. If not an excursion, I would explore doing it on my own - and again, get a taxi driver to give you a tour of the island. The boat to Montserrat leaves out of St. John.
St. Johns, where the cruise ship terminal is located, is not that great of a town to walk around and shop in, IMO - it is very colorful though. Pretty sure whatever the OP does, it will be a great time.