October to march is a good time to visit the Andaman. Nicobar is not allowed for Tourist. and regarding the price, get to Kolkata from Kolkata u can get flights to port blair approximately 3500 for one way and for cruize from port blair to Havelock , or Havelock to neil island or port blair to neil try makcruzz and greenocean cruizes..u can google them..they are very easy to book online. happy travelling.
book hotels and cruize in advance to 3-4 months..
Best time to go there is from Oct to Feb as its too hot during summer. You can go directly to Port Blair airport. There is another way to go to Andaman by Ship from Chennai. But it takes approx 3 -4 days to reach. So its better to go by Air.