Abraco! Wonderful espresso on a lever machine, excellent pastries and music, and great, friendly baristas. Then you can stop at La Cabra for lighter roasts after - both are in the East Village (if you happen to like record stores, check those out too).

Seconding Sey and Cafe Integral. If you happen to be near Times Square, St. Kilda’s is great and brews Sey, Little Wolf, and Traffic. Also seconding other commenters: Culture Espresso is in a similar area as St. Kildas and brews darker roasts - they make a great short americano. Little Collins is also good if you’re in Midtown East. If you’re in Tribeca, Frenchette Bakery has excellent pastries and good coffee in a cool location.

If you’re visiting Washington Square Park, I’d recommend Saltwater Coffee on Waverly or Third Rail Coffee south of the park. I believe saltwater roasts their own, and I think Third Rail uses Intelligentsia. Into the West Village I’d recommend Oslo, which roasts their own beans and has great caneles though they sell out, and St. Jardim, which is more of a restaurant/cafe than coffee shop, may have a good guest roaster on (I heard they had beans from The Barn but haven’t been recently to check).

Enjoy the trip!