You can get tweets from a place if you know the latitude and longitude by using either of these two endpoints:
statuses/filter
search/tweets
For example, using the TwitterAPI Python library:
from TwitterAPI import TwitterAPI
api = TwitterAPI(consumer_key, consumer_secret, access_token_key, access_token_secret)
then
r = api.request('statuses/filter', {'locations':'-74,40,-73,41'})
for item in r:
print(item)
or
r = api.request('search/tweets', {'geocode':'40.5,-73.5,10mi'})
for item in r:
print(item)