yeah i agree with arman, i cant believe i didn't recommend going to little italy and even china town. i think giving directions is good so take the 6 to canal street or bleeker. you could also check out the burton store on spring but it kind of sucks but there is a lot of stores in that general area. you won't be disappointed buying a canoli in little italy, trust me.
taking a walk in central park is fun too and its safe to smoke a joint. i recommend doing it at night and taking in all the views and shit. its amazing. but be safe. not trying to scare you, but its not the safest place haha. take the 6 to 86th through like 59th i believe for the park. basically, the 6 can get you anywhere you need to go.
taking the south ferry is cool too. its free and you can see the statue of liberty and a sick view of the city. thats either the 4 to bowling green i think or the 1 to the last stop.
hope this helps