Well, I am learning that really only Chennai, Havana and Lome are near beaches. Kolkata, Sao Paulo and Manila have great beaches with some travel.
Kolkata has two popular choices for beaches, Shankarpur or the Andaman/Nicobar Islands.
The Andaman and Nicobar Islands are accessible by plane or ship. It is a two hour plane ride. By ship it takes three days. It looks amazing.
Shankarpur is about 100 miles away from Kolkata, accessible by bus or train. The journey takes five hours by bus.
Update: Even though Chennai is near a beach, most generally travel at least an hour to go to a beach where they can enjoy the surf and sand. A friend of mine recently went to the Andaman and Nicobar Islands and said they were amazing. Other friends of ours traveled to Shankarpur, and although it was quite and relaxing, it is not the type of beach to enjoy swimming. One of our friends drew a crowd while there, so unless you crave attention, saving up for the Andaman and Nicobar Islands seems the way to go.