Depends on what are you looking for. If you are a tourist coming to Kolkata for a couple of days, then you should follow the previous answers. But if you are a travel enthusiast, looking for deeper dive into the soul of Kolkata then this answer might help you better.
Metcalfe hall:
This Greek-Doric architecture initially housed the imperial library, now it showcases various artistic sides of Classical calcutta. Very picturesque and wholesome. Though the place is not very big but it’ll certainly leave you amazed. You can easily reach this place by metro. A couple of minutes walk from Mahakaran. Visit between 10am – 5pm
College Street:
There’s a popular phrase roams around people’s mouth here. “If you can’t find a book in college street, then it’s not been published”. Locally known as the “Boi - Para”, college street is the largest second hand book market in the world and among the largest book markets. The energy, the smell of fresh books and debates that floats in the air, makes it special. Where do you think Indian renaissance originated from?
Kumartuli ghat:
Traditionally it used to be the potter’s quarters, Kumartuli is really a photographers paradise. This is where the Gods come into life. Narrow lanes, clay idols that radiates creativity and love, vibrant colors and ofcourse the Ganges river. Best time to visit a few months before Durga puja, although you can visit all year long. Bengalis just don’t stop celebrating.
Dalhousie Square:
The White Town. Built to host the british administrators and merchants with victorian touch. The city got its name City of palaces, mostly because of this region. British colonial architecture took its first steps right here. Victorian Gothic, Indo-Saracenic, Palladian, Georgian.. you can find an array of architectural styles standing right in-front of you. Raj Bhawan, General Post Office, Writers Building, Currency building all are located in this area. Did I mention this is the former capital of India?
Magen David Synagouge:
Being a local, if you trust my words, this is the most beautiful architectural marvel the city possesses, and it can be a bit tricky to find. Located in the busiest area in Kolkata, this jewish synagouge showcases the legacy of the once thriving jewish community that came to Calcutta to make a fortune. Stunning marble floors and stained-glass windows, a high ark that holds the Torah scrolls, ornate chandeliers hanging from the ceiling, and the serenity of the place will leave you astounded.
China Town and Bow Barracks:
Kolkata’s Chinatown is one of the oldest outside China, and Bow Barracks is one of the last Anglo-Indian community pockets in India still thriving with its traditions. Kolkata has always been a safe haven for communities looking for a peaceful life. All the communities that resided here, only added to Kolkata’s rich culture. Breakfast at the China town is a must. You can visit the chinese temples and churches also in the morning. A truly fascinating part of Kolkata where you can see multiple ethnic groups and cultures living together in harmony, complementing each other.
Park street cemetary:
A cemetary? ReallY? I know. This one will sound a bit odd, but trust me on this. One of the oldest non-church cemeteries in the world and among the largest Christian cemeteries outside Europe. The graves are mostly blend of Gothic and Indo-Saracenic architecture, but you’ll see pyramids, obelisks, and Greco-Roman mausoleums surrounded by moss and banyan roots. It’s said to be haunted but I’ve never felt anything (I sit there alone sometime, contemplating life). Best time to visit is during monsoons, when everything gets wrapped with moss and dampening silence, there may not be any ghosts, the atmosphere will surely give you chills.