When in Port Blair or Havelock Island, you can rent a bicycle from the market area. However, it is not possible on other islands. Charges are on a per day basis. The rented bicycles are very basic. You will not get high quality mountain terrain bikes here on which you can do stunts. A motorbike can also be easily rented for the duration of your stay. There are options of non-geared and the geared motorbikes and scooters. The shops renting these bikes will ask for your driving license before you take anything on rent. Charges vary and are on per day basis. You have to bear the fuel charges on your own.
You can be stopped by police personnel for a sudden check. So keep your license with you at all times. Wearing a helmet is mandatory and you will get it with the bike. You will be fined if police stops you and you are not wearing your helmet. Self driven cars are not available for rental but taxi service can be availed for short distances and day hire.