We've been to paradise and decided that anything we'd write is useless. The pictures say everything.
Getting there: Flights to Port Blair are quite cheap if booked in advance from Chennai or Kolkata. Check the ferry times and try to get to Port Blair before midday, otherwise, you'd have to waste a night in the city.
Neil Island: Small and quiet, you one have to relax and enjoy. A much cheaper option.
Getting there: the government ferry (cheaper) is quite irregular but has more free seats for foreigners than the one to Havelock leaving Port Blair. Check ferry times here.
Getting around: Neil is a small island, a rented bike will take you everywhere, just check it well before you leave. We had a flat tire all day long.
Accommodation and dining: Don't book in advance, the best and most affordable places are not connected to the internet, Ajai's Garden has the best vibe, great food, and cheapest huts. Break Water has a great restaurant and lovely huts by the beach. Hidden Garden with only three huts is set in the middle of a quiet and set-back forest, great food and low price. Seashell has the fanciest cottages and well-kept garden, come just for their affordable breakfast to feel fancy. Check some options online on go2andaman.com
Havelock: More developed and visited, better beaches and scuba diving.
Getting there: government ferries get sold extremely fast (within hours, 3 days in advance), try with an agent or you'll have to buy the private ferry.
Getting around: Renting a scooter is the best option, there's a bus from the jetty, through the market to beach number 7 and the entrance to the Elephant Beach path.
Accommodation: There are plenty of small huts along beach number 5, mostly ill maintained and dirty. Collect a couple of names from goandaman.com and ask a rickshaw driver to take you there, check each one and then decide, don't let the driver persuade you otherwise, they have contacts with hostels. don't pay more that 100 rupees.
Dining out: Anju Coco is packed with Israelis and great food for a good price. For great and affordable seafood go for Squid in the market. The best thali at the lowest price is Deepak, on the side street of the jetty.