Most fun place for nerdy East coast guys to go. We like Jamaican beef Patty's, boardgames and back to the future
Okay, I love this question because you're not asking for a generic "fun city" recommendation, you're painting a real picture of yourselves, and that actually narrows this down nicely.
My top call for you is New York City, specifically the combination of lower Manhattan and Brooklyn. Before you roll your eyes at the obvious answer, hear me out, because for this particular set of interests, nowhere else on the East Coast comes close. The Jamaican beef patty situation in New York is genuinely world-class. Golden Crust is the institution, with locations all over Brooklyn and the Bronx, and the patties there are the real deal, flaky, spiced, stuffed properly. Brooklyn in particular has a deep Jamaican community and the food reflects it. For board games, Hex & Co. in Manhattan is the gold standard of East Coast board game cafes, enormous library, smart staff who can actually teach you games, and a genuinely fun atmosphere that doesn't take itself too seriously. Brooklyn also has Rook's Corner, which draws a more local crowd and has a great selection of heavier strategy games if that's your thing.
The Back to the Future angle is where New York truly seals the deal, because the musical adaptation has been running on Broadway and it is a genuinely spectacular production, a perfect mix of nostalgia, spectacle, and nerdy enthusiasm. Even if you've seen it, seeing it in a Broadway house with a crowd of fellow fans is its own experience. Beyond that, New York has the kind of pop culture density that rewards curious, enthusiastic people: record shops, vintage stores, comic shops in the East Village, and enough niche culture that you'll keep stumbling onto things that feel made for you.
If you want something smaller-scale and a little more curated, Providence, Rhode Island is worth serious consideration. It's a college town with a strong nerd culture infrastructure, great game shops, a thriving indie food scene, and a compact walkable downtown where you can bounce between spots easily. The Jamaican food options are fewer, but the overall atmosphere of a city that fully embraces its own eccentricities makes it a great weekend destination. It's also easy to combine with a Boston day trip, which has its own excellent game cafes and a surprising Caribbean food scene in Dorchester.