One of my favorite short vacation destination is a place called Mandarmani. It is a seaside resort village. To travel to it, you can take a bus/car ride from Calcutta which will take you 4 hours.
I like it because the beach is nice and there are generally not many people. It is very different to the more famous Digha beach, there are just too many people around there. The hotels are all close to the beach itself, so you will get a great view and good breeze. The food served is very tasty if you like Bengali cuisine. One downside though is for what the hotel provides its a bit expensive.
There is nothing for sightseeing, it’s just beach, you can see some crabs but that’s it. If you just want to chill it’s an ideal place.