If you're flying, dont forget to keep a good book for company.
There are direct flights but no direct trains for this journey. Hyderabad (Andhra Pradesh) to Port Blair (Andaman And Nicobar Islands) distance is 1661 km and you can get there by flight in just over 4 hours and 40 minutes or by train + flight fares starting from ₹ 3512.
The weather is amazing right now. You'll have a great time.