History + technical museums:

I’d recommend the AMNH and the Intrepid personally, I think they’re both full of cool stuff.

Food, as others have said, so many options. Doesn’t have to be expensive in any way shape or form, there’s a ton of food from any culture there. If you’re in Manhattan (assuming so tourism wise?) Korea town and China Town have tons of authentic food.

Social: chat away, especially at bars. It’s refreshing to see someone wanting that, not trying to avoid it :) it’s a city with loads of friendly people in my opinion.

Have fun!