I went to Antigua about 3 years ago (2 adults, 2 kids) and we hired a car for the day and done the sights and got to see lots more of the island too. It cost us about $100 at the time.

I would also advise doing your own thing, as you can go at your own pace. I was in Antigua about 1½ years ago and booked a car + driver for an afternoon, through my rep and hotel. I seem to remember they had a few set itineraries but were more than willing to swap things around to suit what I wanted to do. It cost me $70 though I managed to negotiate a discount as I was on my own - I think it helped that it was low season at the time as well! I think the normal price was around $100.

As you're visiting from a cruise though I expect you probably won't want to waste time negotiating prices with taxi drivers. It may be worth contacting tourist services over there in advance to see if they could prebook you something. My tour operator used St James Travel in Antigua for their rep and transfer services. I don't know it they'll be able to help or even offer you the best price but if you'd like to contact them for info, their email is antigua@stjamesgroup.com

Hope this helps and enjoy your trip