Assign NTA's to lat longs using R?

You are looking for an spatial join, after converting your lat-longs to a spatial object. This is done easily with package sf, replace the filenames with yours on the following code:

library(sf)
library(dplyr)
lat_longs = read.csv(latlongs.csv) %>% 
     st_as_sf(coords = c("longitude_column", "latitude_column")) %>% 
     st_set_crs(4326) # coordinate reference system is lat-long
NTA = read_sf("nta_polygons.shp")

lat_longs_NTA = lat_longs %>% st_join(NTA)