On reaching Port Blair, I would highly recommend heading straight to the hotel from the airport and getting ready as soon as possible to step out to explore the city of Port Blair.
There are many options of commuting within Port Blair ranging from private cabs to even local buses, stopping right outside the airport, or you can even ask your hotel to pick you up from the airport.
For moving in and around the city, you can even rent a two wheeler or a cab.
Also, in case you want to book your Ferry tickets to Havelock or any other island in Andaman in advance, you can do that here at the airport as there are counters of Makruzz and Sea Link at the airport.
There are many things to do in Port Blair from trekking at Chidiya Tapu to catching a beautiful sunset or exploring the Ross Island.
Here is a list of things that you can do while in Port Blair.
Since, I was on a comparatively tight schedule, just half a day to be honest, I preferred to visit only those places that I wanted to explore and leave the rest for another time.
Well, traveling solo has an advantage to pick and choose according to one's own whims.