Half Moon is a secluded beach, but no facilities, no beds etc., with good, but variable, snorkelling to the far left when looking out to sea.
On first visit, just exploring by oneself one will miss out on so many places, the history, culture, etc.
Consider a group tour with Lawrence of Antigua, taking in the sights etc., then while driving note a beach or two of interest for one’s next visit. Popular (ease of reach) beaches will always be busy, leaving the more upmarket venues alone (published in many posts)
If of interest, there is a recent exchange on AI resort (previously overlooked)
Lastly, if there is a special treat required, take a look at a Rock Pool day at Sheer Rocks, can confirm it’s a luxurious pampering day, with truly wonderful views. The ambiance, food, drinks and service are excellent.
Hope one finds something. No doubt other CC members will post to assist.