This is how my itinerary was:
Port Blair - 2 nights
Havelock -2 nights
Neil Island - 1 night
I did scuba dive in Neil island and snorkelling in Havelock. was worth it. do try it out.
Stay in Aberdeen Bazar in port blair. Being centrally located it is the best place to stay. There's this star hotel near Annapurna Cafeteria which is a really cheap and good hote. Annapurna Cafeteria has best food.
You can visit:
Havelock island
Rose and viper island
Take 1 day package from Andaman tourism for Jarwa tribe, limestone caves, mud volcano etc.
Neil island
must go for scuba diving/snorkeling