Hey Adi,
You can always plan your own itinerary ...
Both in port Blair and in Havelock you get bikes for rent in 500 rupees per day and stay options you can book homestays in both the places ...
All you need to worry is about booking cruise from port Blair to Havelock and then from Havelock to Neil island and then from Neil island to all the way back to port Blair ...
Pre book your slots depending on your itinerary here on makruzz link directly for all the islands they offer the cruise ....
They are best in business in Andaman ...
http://www.makruzz.com/site/
And for itinerary you would need a sweet 5 days to cover all the three islands ....
Day 1 and 2 :- Port Blair
Corbyn's cove beach
Veer savarkar jail
Chidiya tapu beach
Vandoor beach
Marine museum
Day 3 and 4 :-
Havelock island
Scuba diving near Hetty in Havelock island
Sunset in Radhanagar beach
Elephant beach Trekking
Kalapathar beach for a pic in your Instagram
Day 5 :- Neil island
A pic at natural bridge ...
A roam around the beaches
And then cruise back to port Blair from Neil and leave pory nalir the same day ...
See that it's always best to take an early morning flight to port Blair and also an exit on early morning from port Blair as the airport doesn't welcome flights post 4 on the evening ....
Happy Travelling Bro!!!
Package will be safe option, but If you want something different, then don't make any particular plan. but you should stay for 2-3 days for Havelock. beaches are awesome. you feel relaxed at that place..
Best option go by yourself. travel agents don't cover offbeat places that really amazing to experience. for itinerary visit my Andaman tour blog here. and of course you can enjoy very cheaply than agents. take min. 8-9 days if you really want to visit offbeat places. and most important is that you will never be cheated there.
Best to get a package from a travel consultant...they will help you grab the best deals n discounts n plus can modify the itineary according to your preferences...???? reply for getting details...
The best thing would be to book your first stop hotel, and then the rest you can do while you are there as it is never full and always place available to go to various island tours etc.