The Andaman Islands are the closest thing India has to a tropical island holiday: clear water, coral, white sand and very little development outside Port Blair and Havelock. The catch is access and seasonality — ferries stop in the monsoon and the whole plan depends on which islands are open.
October to May is the season. November to February is the most comfortable, with calm seas and good visibility. March to May is hotter but still workable and slightly cheaper. June to September is the southwest monsoon: inter-island ferries are frequently cancelled, many resorts close, and diving operators shut down. Do not book a monsoon Andaman trip expecting to island-hop.
Flights connect Port Blair with Chennai, Kolkata, Delhi and Bengaluru. The alternative is a two to three day ship from Chennai or Kolkata, which is an experience rather than a convenience. From Port Blair, ferries and catamarans run to Havelock (Swaraj Dweep) and Neil (Shaheed Dweep), and those bookings should be made in advance for peak season.
Mobile connectivity is patchy outside Port Blair, so do not plan to work remotely from Havelock. Carry cash, because ATMs are limited and unreliable. Alcohol licensing is restricted on some islands. And keep the last night in Port Blair before your flight home — a cancelled ferry on the final day is the most common way an Andaman trip goes wrong.
See the Andaman tour package for a fixed itinerary including ferries and transfers.