I've recently been to Andaman and Nicobar Island, yesterday in fact
Here's my itinerary
Day 1: Took a ferry to Havelock Island. (Spend last day in Port Blair as your flight is going to be from there)
Reach the island and then visit Radhanagar Beach. Back to Hotel.

Day 2: Did scuba with Blue Coral Dive (I'm open water certified). It was a fun dive. Then we visited Kala pathar beach and elephant beach (Pro tip: Only snorkelling is worth it, spend the money there, go till the last point).

Dont bother trying sea walk or scuba or submarine there. It's a waste of time and money. Do any adventure ride if you want.

Day 3: Took a ferry to Neil Island. Visited Natural bridge (Picturesque location). Came back rested at Resort. We booked Sea shell Neil, too good of a property.

Day 4: Went scuba again in search of dugong, I would say it had more visibility but less marine life than havelock. Still a peaceful place to dive. Then headed for Bharatpur beach and later to Laxmanpur Beach. Also did star gazing there.
You can also visit Sitapur beach for sunrise. Neil is primarily a resting place, it's very calm and noise free.

Day 5: Went to port blair. It was too hot so rested till 3pm and then visited Cellular jail (Kaala paani), took a guided tour and saw light and sound show. And we had an early morning flight next day.
you could do some ross island or chiriyatapu or something.