Ask anyone who's lived in Kolkata in his or her youth, and the one food they hanker for is the Kolkata Roll. Mustard fish, rossogolla. puchka, jhalmuri, all have undoubted appeal, but the most universal of the lot is the kati roll. Everyone except a dietician loves it.
I don't visit Kolkata that much anymore, but its been my fortune to find the Kolkata roll becoming Bengal's biggest food export. New York, in particular, developed rather nicely as a roll destination; there were none when I moved there, now there are at least six. The most famous one - Kati Roll Company - is so popular it employs bouncers to keep the queues orderly. Other good choices, in order of preference are Indian Bread Company and Roomali, but nowadays Yelp lists over a dozen!!
Mumbai had its own pretender - the Frankie invented by Tibb (whose son was briefly in college with me). However, the frankie is rolled in a naan rather than a paratha and filled with all manners of gooey curries (no barbecue here) basically a poor substitute for the Kolkata roll-seeker. My favourite roll place in Mumbai is Hangla's, at the edge of Lokhandwala Market. It churns out Kolkata rolls that would be a hit even in Kolkata - huge, greasy and utterly delicious. A little bit further away on JP Road, near the Gurudwara, is the much more unassuming Bhima's -its a true streetcart, also good but somewhat inferior to Hangla (avoid anything else but rolls there, though). Another roll vendor in Lokhandwala Market is better avoided altogether. A new kid on the block is Kolkata Konnection, just opened a couple of weeks ago across the road from Mega Mall - good filling, outstanding parathas.
Bandra has Calcutta Roll Centre (nearly impossible to find now behind a Marathi signboard) - across the road from Amarsons on Linking Road. They sell rolls filled with gravy chicken or mutton rather than kati kababs; good but more like parathas and gravy than real rolls. A new challenger in Bandra is Dee's Roll Center, sandwiched between two stalwarts of Hill Road - American Express Bakery and A1 Bakery. They make very good rolls - parathas filled with fat, spicy tangy kati kababs. They also have a long and very popular line of chinese dishes, and some very avoidable kassa (supposedly from the Nizams of Bengal, whoever they are) but their rolls are indeed quite good.
Versova has another roll seller, though more Lucknow in origin that Kolkata. Lazaat-e-Lucknow sells great paratha rolls, only they use gilawati kababs and Lucknow-style ulta-tawa parathas instead of lacchedar parathas. If you're willing to venture further, Kakori Hut in Bandra does a superior version of the same thing.
Then, there's the roomali roll. Bengalis don't really consider them real rolls, but they have their place. Most places make very poor roomali rolls (usually because they're peddling health food) but there are exceptions. My favourite roomali roll vendor is Bangalore's famous Fanoos, especially their five-seekh monster of a Mambo roll, with about two inches of beef to a millimetre of roti. Wraps & Rolls has outlets in major malls and makes fairly decent rolls in a huge number of filling options.