Check out El Museo del Barrio in Manhattan. (www.elmuseo.org) Or maybe see if you can get tickets to see In the Heights on Broadway. Parts are in Spanish and it does discuss Cuban, Dominican, and Puerto Rican culture. There is the Thalia Spanish Theatre in Sunnyside, Queens. (www.queensnewyork.com/cultural/thalia)Or check out the Nuyorican Poets Cafe in the East Village. (www.nuyorican.org) They have poetry slams, latin jazz nights, and plays by local writers. (Right now there s a reading scheduled for Dec. 21 by a host of Latino writers, and a comedy show advertised as trilingual .) Just call to make sure that teens would be allowed in before you go, since after a certain time it doubles as a bar. For restaurants, check out Havana Central in Times Square or Son Cubanos in the meat packing district. Both have delicious cuban food and live music (salsa, merengue, etc.).
Go to a play here: http://www.repertorio.org/.