How can I search tweets on twitter by hashtag, date, and/or location?

[xander]

I am looking to develop a map of twitter activity in Manhattan during Hurricane Sandy last year. I plan to use Leaflet to develop the map, and have the script to pull geotags off each tweet individually (though that will be a real nightmare), but I can't find a good API or general method to gather the tweets in my date/time range. I am good on HTML5 and CSS3, and, while I don't know much Java, would be willing to learn what I need to there. Any suggestions on how I can find tweets that occurred on Manhattan on that day with the appropriate hashtags? Again, I'm happy to extract the geotags one by one and paste them into Leaflet if I have to.